Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Precalculus Enhanced with Graphing Utilities
In Problems 89-112, solve each equation. log 3 (3x2)=2In Problems 89-112, solve each equation. log x 4=2In Problems 89-112, solve each equation. log x ( 1 8 )=3In Problems 89-112, solve each equation. ln e x =5In Problems 89-112, solve each equation. ln e 2x =8In Problems 89-112, solve each equation. log 4 64=xIn Problems 89-112, solve each equation. log 5 625=xIn Problems 89-112, solve each equation. log 3 243=2x+1In Problems 89-112, solve each equation. log 6 36=5x+3In Problems 89-112, solve each equation. e 3x =10In Problems 89-112, solve each equation. e 2x = 1 3In Problems 89-112, solve each equation. e 2x+5 =8In Problems 89-112, solve each equation. e 2x+1 =13In Problems 89-112, solve each equation. log 3 ( x 2 +1 )=2In Problems 89-112, solve each equation. log 5 ( x 2 +x+4 )=2In Problems 89-112, solve each equation. log 2 8 x =3In Problems 89-112, solve each equation. log 3 3 x =1In Problems 89-112, solve each equation. 5 e 0.2x =7In Problems 89-112, solve each equation. 8 10 2x7 =3In Problems 89-112, solve each equation. 2 10 2x =5In Problems 89-112, solve each equation. 4 e x+1 =5Suppose that G( x )= log 3 ( 2x+1 )2 . a. What is the domain of G ? b. What is G( 40 ) ? What point is on the graph of G ? c. If G(x)=3 , what is x ? What point is on the graph of G ? d. What is the zero of G ?Suppose that F(x)= log 2 ( x+1 )3 . a. What is the domain of F ? b. What is F( 7 ) ? What point is on the graph of F ? c. If F(x)=1 , what is x ? What point is on the graph of F ? d. What is the zero of F ?In Problems 115-118, graph each function. Based on the graph, state the domain and the range, and find any intercepts. f( x )={ lnx ln(x) ifx0 ifx0In Problems 115-118, graph each function. Based on the graph, state the domain and the range, and find any intercepts. f(x)={ ln(x) ln(x) if1x0 ifx1In Problems 115-118, graph each function. Based on the graph, state the domain and the range, and find any intercepts. f(x)={ lnx lnx ifx1 if0x1In Problems 115-118, graph each function. Based on the graph, state the domain and the range, and find any intercepts. f(x)={ lnx lnx ifx1 if0x1117AYU118AYU119AYU120AYU121AYU122AYU123AYU124AYU125AYU126AYU127AYU128AYU129AYU130AYU131AYU132AYU133AYU134AYU135AYU136AYU1AYU2AYU3AYU4AYU5AYU6AYU7AYU8AYU9AYU10AYU11AYU12AYU13AYU14AYU15AYU16AYU17AYU18AYU19AYU20AYU21AYU22AYU23AYU24AYU25AYU26AYU27AYU28AYU29AYU30AYU31AYU32AYU33AYU34AYU35AYU36AYU37AYU38AYU39AYU40AYU41AYU42AYUIn Problems 37-56, write each expression as a sum and/or difference of logarithms. Express powers as factors. ln x e xIn Problems 37-56, write each expression as a sum and/or difference of logarithms. Express powers as factors. ln( x e x )In Problems 37-56, write each expression as a sum and/or difference of logarithms. Express powers as factors. log a ( u 2 v 3 )u0,v0In Problems 37-56, write each expression as a sum and/or difference of logarithms. Express powers as factors. log 2 ( a b 2 )a0,b0In Problems 37-56, write each expression as a sum and/or difference of logarithms. Express powers as factors. ln( x 2 1x )0x1In Problems 37-56, write each expression as a sum and/or difference of logarithms. Express powers as factors. ln(x 1+ x 2 )x0In Problems 37-56, write each expression as a sum and/or difference of logarithms. Express powers as factors. log 2 ( x 3 x3 )x3In Problems 37-56, write each expression as a sum and/or difference of logarithms. Express powers as factors. log 5 ( x 2 +1 x 2 1 3 )x1In Problems 37-56, write each expression as a sum and/or difference of logarithms. Express powers as factors. log[ x(x+2) (x+3) 2 ]x0In Problems 37-56, write each expression as a sum and/or difference of logarithms. Express powers as factors. log[ x 3x+1 ( x2 ) 2 ]x2In Problems 37-56, write each expression as a sum and/or difference of logarithms. Express powers as factors. ln [ x 2 x2 ( x+4 ) 2 ] 1/3 x2In Problems 37-56, write each expression as a sum and/or difference of logarithms. Express powers as factors. ln [ (x4) 2 x 2 1 ] 2/3 x4In Problems 37-56, write each expression as a sum and/or difference of logarithms. Express powers as factors. ln 5x 1+3x (x4) 3 x4In Problems 37-56, write each expression as a sum and/or difference of logarithms. Express powers as factors. ln[ 5 x 2 1x 3 4 (x+1) 2 ]0x1In Problems 57-70, write each expression as a single logarithm. 3 log 5 u+4 log 5 vIn Problems 57-70, write each expression as a single logarithm. 2 log 3 u log 3 vIn Problems 57-70, write each expression as a single logarithm. log 3 x log 3 x 3In Problems 57-70, write each expression as a single logarithm. log 2 ( 1 x )+ log 2 ( 1 x 2 )In Problems 57-70, write each expression as a single logarithm. log 4 ( x 2 1)5lo g 4 (x+1)In Problems 57-70, write each expression as a single logarithm. log( x 2 +3x+2)2log(x+1)In Problems 57-70, write each expression as a single logarithm. ln( x x1 )+ln( x+1 x )ln( x 2 1)In Problems 57-70, write each expression as a single logarithm. log( x 2 +2x3 x 2 4 )log( x 2 +7x+6 x+2 )In Problems 57-70, write each expression as a single logarithm. 8 log 2 3x2 lo g 2 ( 4 x )+ log 2 4In Problems 57-70, write each expression as a single logarithm. 21 log 3 x+ log 3 (9 x 2 )lo g 3 9 3In Problems 57-70, write each expression as a single logarithm. 2 log a (5 x 3 ) 1 2 log a (2x+3)In Problems 57-70, write each expression as a single logarithm. 1 3 log( x 3 +1)+ 1 2 log( x 2 +1)In Problems 57-70, write each expression as a single logarithm. 2 log 2 (x+1)lo g 2 (x+3)lo g 2 (x1)In Problems 57-70, write each expression as a single logarithm. 3 log 5 (3x+1)2lo g 5 (2x1)lo g 5 xIn Problems 71-78, use the Change-of-Base Formula and a calculator to evaluate each logarithm. Round your answer to three decimal places. log 3 21In Problems 71-78, use the Change-of-Base Formula and a calculator to evaluate each logarithm. Round your answer to three decimal places. log 5 18In Problems 71-78, use the Change-of-Base Formula and a calculator to evaluate each logarithm. Round your answer to three decimal places. log 1/3 71In Problems 71-78, use the Change-of-Base Formula and a calculator to evaluate each logarithm. Round your answer to three decimal places. log 1/2 15In Problems 71-78, use the Change-of-Base Formula and a calculator to evaluate each logarithm. Round your answer to three decimal places. log 2 7In Problems 71-78, use the Change-of-Base Formula and a calculator to evaluate each logarithm. Round your answer to three decimal places. log 5 8In Problems 71-78, use the Change-of-Base Formula and a calculator to evaluate each logarithm. Round your answer to three decimal places. log eIn Problems 71-78, use the Change-of-Base Formula and a calculator to evaluate each logarithm. Round your answer to three decimal places. log 2In Problems 79-84, graph each function using a graphing utility and the Change-of-Base Formula. y= log 4 xIn Problems 79-84, graph each function using a graphing utility and the Change-of-Base Formula. y= log 5 xIn Problems 79-84, graph each function using a graphing utility and the Change-of-Base Formula. y= log 2 (x+2)In Problems 79-84, graph each function using a graphing utility and the Change-of-Base Formula. y= log 4 (x3)In Problems 79-84, graph each function using a graphing utility and the Change-of-Base Formula. y= log x1 (x+1)In Problems 79-84, graph each function using a graphing utility and the Change-of-Base Formula. y= log x+2 (x2)If f(x)=lnx , lnx,g(x)= e x , and h(x)= x 2 , find: (a) (fg)(x) What is the domain of fg ? (b) (gf)(x) What is the domain of gf ? (c) (fg)(5) (d) (fh)(x) What is the domain of fh ? (e) (fh)(e)If f(x)= log 2 x , g(x)= 2 x , and h(x)=4x , find: (a) (fg)(x) What is the domain of fg ? (b) (gf)(x) What is the domain of gf ? (c) (fg)(3) (d) (fh)(x) What is the domain of fh ? (e) (fh)(8)In Problems 87-96, express y as a function of x. The constant C is a positive number. lny=lnx+lncIn Problems 87-96, express y as a function of x. The constant C is a positive number. lny=ln(x+c)In Problems 87-96, express y as a function of x. The constant C is a positive number. lny=lnx+ln(x+1)+lncIn Problems 87-96, express y as a function of x. The constant C is a positive number. lny=2lnxln(x+1)+lnCIn Problems 87-96, express y as a function of x. The constant C is a positive number. lny=3x+lnCIn Problems 87-96, express y as a function of x. The constant C is a positive number. lny=2x+lnCIn Problems 87-96, express y as a function of x. The constant C is a positive number. ln(y3)=4x+lnCIn Problems 87-96, express y as a function of x. The constant C is a positive number. ln(y+4)=5x+lnCIn Problems 87-96, express y as a function of x. The constant C is a positive number. 3lny= 1 2 ln(2x+1) 1 3 ln(x+4)+lnCIn Problems 87-96, express y as a function of x. The constant C is a positive number. 2lny= 1 2 lnx+ 1 3 ln( x 2 +1)+lnCFind the value of log 2 3 log 3 4 log 4 5 log 5 6 log 6 7 log 7 8 .Find the value of log 2 4 log 4 6 log 6 8 .Find the value of log 2 3 log 3 4 log n (n+1) log n+1 2 .Find the value of log 2 2 log 2 4 log 2 2 n .Show that log a (x+ x 2 1 )+lo g a (x x 2 1 )=0 .Show that log a ( x + x1 )+lo g a ( x x1 )=0 .Show that ln(1+ e 2x )=2x+ln(1+ e 2x ) .Difference Quotient If f(x)=lo g a x , show that f(x+h)f(x) h = log a ( 1+ h x ) 1/h ,h0 .If f(x)=lo g a x , show that f(x)=lo g 1/a x .If f(x)=lo g a x107. If f(x)=lo g a x , show that f( 1 x )=f(x)108. If f(x)=lo g a x , show that f( x )=f(x)109. Show that log a ( M N )= log a Mlo g a N , where a, M, and N are positive real numbers and a1110. Show that log a ( 1 N )= log a N , where a and N are positive real numbers and a1 .111. Graph Y 1 =log( x 2 ) and Y 2 =2log(x) using a graphing utility. Are they equivalent? What might account for any differences in the two functions?112. Write an example that illustrates why (lo g a x) r rlo g a x .113. Write an example that illustrates why log 2 (x+y)lo g 2 x+lo g 2 y .114. Does 3 log 3 (5)=5 ? Why or why not?Solve x 2 7x30=0 . (pp.A47-A52)Solve (x+3) 2 4(x+3)+3=0 .(pp. A52-A53)Approximate the solution(s) to x 3 = x 2 5 using a graphing utility. (pp. 26-28)Approximate the solution(s) to x 3 2x+2=0 using a graphing utility. (pp. 26-28)ln Problems 5-40, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. log 4 x=2ln Problems 5-40, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. log( x+6 )=1ln Problems 5-40, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. log 2 ( 5x )=4ln Problems 5-40, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. lo g 3 ( 3x1 )=2ln Problems 5-40, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. log 4 ( x+2 )= log 4 8ln Problems 5-40, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. lo g 5 ( 2x+3 )=lo g 5 3ln Problems 5-40, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 1 2 log 3 x=2 log 3 2ln Problems 5-40, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 2 log 4 x= log 4 9ln Problems 5-40, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 3 log 2 x= log 2 27ln Problems 5-40, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 2 log 5 x=3 log 5 4ln Problems 5-40, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 3 log 2 ( x1 )+ log 2 4=5ln Problems 5-40, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 2 log 3 ( x+4 ) log 3 9=2ln Problems 5-40, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. logx+log( x+15 )=2ln Problems 5-40, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. logx+log( x21 )=2ln Problems 5-40, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. log( 2x+1 )=1+log( x2 )ln Problems 5-40, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. log( 2x )log( x3 )=1ln Problems 5-40, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. log 2 ( x+7 )+ log 2 ( x+8 )=1ln Problems 5-40, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. log 6 ( x+4 )+ log 6 ( x+3 )=1ln Problems 5-40, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. log 8 ( x+6 )=1 log 8 ( x+4 )ln Problems 5-40, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. log 5 ( x+3 )=1 log 5 ( x1 )ln Problems 5-40, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. lnx+ln( x+2 )=4ln Problems 5-40, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. ln( x+1 )lnx=2ln Problems 5-40, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. log 3 ( x+1 )+ log 3 ( x+4 )=2ln Problems 5-40, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. log 2 ( x+1 )+ log 2 ( x+7 )=3ln Problems 5-40, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. log 1/3 ( x 2 +x ) log 1/3 ( x 2 x )=1ln Problems 5-40, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. log 4 ( x 2 9 ) log 4 ( x+3 )=3ln Problems 5-40, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. log a ( x1 ) log a ( x+6 )= log a ( x2 ) log a ( x+3 )ln Problems 5-40, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. log a x+ log a ( x2 )= log a ( x+4 )In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 2 x5 =8In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 5 x =25In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 2 x =10In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 3 x =14In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 8 x =1.2In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 5( 2 3x )=8In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 5 x =25In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 0.3( 4 0.2x )=0.2In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 3 12x = 4 xIn Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 2 x+1 = 5 12xIn Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. ( 3 5 ) x = 7 1xIn Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. ( 4 3 ) 1-x = 5 xIn Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 1.2 x = ( 0.5 ) xIn Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 0.3 1+x = 1.7 2x1In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 1-x = e xIn Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. e x+3 = xIn Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 2 2x + 2 x 12=0In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 3 2x + 3 x 2=0In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 3 2x + 3 x+1 4=0In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 2 2x + 2 x+2 12=0In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 16 x + 4 x+1 3=0In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 9 x 3 x1 +1=0In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 25 x 8.5 x =16In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 36 x 6.6 x =9In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 3.4 x + 4.2 x +8=0In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 2.49 x + 11.7 x +5=0In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 4 x 10.4 x =3In Problems 41-68, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 3 x 14.3 x =5In Problems 69-82, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. log 5 ( x+1 ) log 4 ( x2 )=1In Problems 69-82, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. log 2 ( x1 ) log 6 ( x+2 )=2In Problems 69-82, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. e x =xIn Problems 69-82, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. e 2x =x+2In Problems 69-82, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. e x = x 2In Problems 69-82, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. e x = x 3In Problems 69-82, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. lnx=xIn Problems 69-82, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. ln( 2x )=x+2In Problems 69-82, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. lnx= x 3 1In Problems 69-82, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. lnx= x 2In Problems 69-82, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. e x +lnx=4In Problems 69-82, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. e x lnx=4In Problems 69-82, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. e x =lnxIn Problems 69-82, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. e x =lnxIn Problems 83-94, solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. log 2 ( x+1 ) log 4 x=1 [Hint: Change log 4 x to base 2.]In Problems 83-94, solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. log 2 ( 3x+2 ) log 4 x=3In Problems 83-94, solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. log 16 x+ log 4 x+ log 2 x=7In Problems 83-94, solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. log 9 x+3 log 3 x=14In Problems 83-94, solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. ( 2 3 ) 2x = 2 x 2In Problems 83-94, solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. log 2 x log 2 x =4 [Hint: Change log 4 x to base 2.]In Problems 83-94, solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. e x + e x 2 =1 [Hint: Multiply each side by e x .]In Problems 83-94, solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. e x + e x 2 =3In Problems 83-94, solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. e x e x 2 =2In Problems 83-94, solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. e x e x 2 =2In Problems 83-94, solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. log 5 x+ log 3 x=1 [Hint: Use the Change-of-Base Formula.]In Problems 83-94, solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. log 2 x log 6 x=3f( x )= log 2 ( x+3 ) and g( x )= log 2 ( 3x+1 ) . (a) Solve f( x )=3 . What point is on the graph of f ? (b) Solve g( x )=4 . What point is on the graph of g ? (c) Solve f( x )=g( x ) . Do the graphs of f and g intersect? If so, where? (d) Solve ( f+g )( x )=7 . (e) Solve ( fg )( x )=2f( x )= log 3 ( x+5 ) and g( x )= log 3 ( x1 ) (a) Solve f( x )=2 . What point is on the graph of f ? (b) Solve g( x )=3 . What point is on the graph of g ? (c) Solve f( x )=g( x ) . Do the graphs of f and g intersect? If so, where? (d) Solve ( f+g )( x )=3 . (e) Solve ( fg )( x )=2 .(a) If f( x )= 3 x+1 and g( x )= 2 x+2 , graph f and g on the same Cartesian plane. (b) Find the point(s) of intersection of the graphs of f and g by solving f( x )=g( x ) . Round answers to three decimal places. Label any intersection points on the graph drawn in part (a). (c) Based on the graph, solve f( x )g( x ) .(a) If f( x )= 5 x1 and g( x )= 2 x+1 , graph f and g on the same Cartesian plane. (b) Find the point(s) of intersection of the graphs of f and g by solving f( x )=g( x ) . Label any intersection points on the graph drawn in part (a). (c) Based on the graph, solve f( x )g( x ) .(a) Graph f( x )= 3 x and g( x )=10 on the same Cartesian plane. (b) Shade the region bounded by the y-axis , f( x )= 3 x and g( x )=10 on the graph drawn in part (a). (c) Solve f( x )=g( x ) and label the point of intersection on the graph drawn in part (a).(a) Graph f( x )= 2 x and g( x )=12 on the same Cartesian plane. (b) Shade the region bounded by the y-axis , f( x )= 2 x and g( x )=12 on the graph drawn in part (a). (c) Solve f( x )=g( x ) and label the point of intersection on the graph drawn in part (a).(a) Graph f( x )= 2 x+1 and g( x )= 2 x+2 on the same Cartesian plane. (b) Shade the region bounded by the y-axis , f( x )= 2 x+1 and g( x )= 2 x+2 on the graph drawn in part (a). (c) Solve f( x )=g( x ) and label the point of intersection on the graph drawn in part (a).(a) Graph f( x )= 3 x+1 and g( x )= 3 x2 on the same Cartesian plane. (b) Shade the region bounded by the y-axis, f( x )= 3 x+1 and g( x )= 3 x2 on the graph drawn in part (a). (c) Solve f( x )=g( x ) and label the point of intersection on the graph drawn in part (a).(a) Graph f( x )= 2 x 4 . (b) Find the zero of f . (c) Based on the graph, solve f( x )0 .(a) Graph g( x )= 3 x 9 . (b) Find the zero of g . (c) Based on the graph, solve g( x )0 .A Population Model The resident population of the United States in 2015 was 320 million people and was growing at a rate of 0.7 per year. Assuming that this growth rate continues, the model P( t )=320 ( 1.007 ) t2015 represents the population P (in millions of people) in year t . (a) According to this model, when will the population of the United States be 400 million people? (b) According to this model, when will the population of the United States be 435 million people? Source: U.S Census BureauA Population Model The population of the world in 2015 was 7.21 billion people and was growing at a rate of 1.1 per year. Assuming that this growth rate continues, the model P( t )=7.21 ( 1.011 ) t2015 represents the population P (in billions of people) in year t . (a) According to this model, when will the population of the world be 9 billion people? (b) According to this model, when will the population of the world be 12.5 billion people? Source: U.S Census BureauDepreciation The value V of a Chevy Cruze LS that is t years old can be modeled by V( t )=18,700 ( 0.84 ) t (a) According to the model, when will the car be worth 9000 ? (b) According to the model, when will the car be worth 6000 ? (c) According to the model, when will the car be worth 2000 ? Source: Kelley Blue BookDepreciation The value V of a Honda Civic SE that is t years old can be modeled by V( t )=18,955 ( 0.905 ) t . (a) According to the model, when will the car be worth 16,000 ? (b) According to the model, when will the car be worth 10,000 ? (c) According to the model, when will the car be worth 7500 ? Source: Kelley Blue BookFill in the reason for each step in the following two solutions. Solve: log 3 ( x1 ) 2 =2 Solution A log 3 ( x1 ) 2 =2 ( x1 ) 2 = 3 2 =9 ( x1 )=3 x1=3 or x1=3 x=2 or x=4 Solution B log 3 ( x1 ) 2 =2 2 log 3 ( x1 )=2 log 3 ( x1 )=1 x1= 3 1 =3 x=4 Both solutions given in Solution A check. Explain what caused the solution x=2 to be lost in Solution B.What is the interest due if 500 is borrowed for 6 months at a simple interest rate of 6 per annum? (pp. A67-A68)If you borrow 5000 and, after 9 months, pay off the loan in the amount of 5500 , what per annum rate of interest was charged? (pp. A67-Α68)The total amount borrowed (whether by an individual from a bank in the form of a loan or by a bank from an individual in the form of a savings account) is called the _____________________.If a principal of P dollars is borrowed for a period of t years at a per annum interest rate r , expressed as a decimal, the interest I charged is = . Interest charged according to this formula is called ____ _____.In working problems involving interest, if the payment period of the Interest is quarterly, then interest is paid ____ times per year.The ___ ___ ___ ___ is the equivalent annual simple interest rate that would yield the same amount as compounding n times per year, or continuously, after 1 year.In Problems 7-14, find the amount that results from each investment. 100 invested at 4 compounded quarterly after a period of 2 yearsIn Problems 7-14, find the amount that results from each investment. 50 invested at 6 compounded monthly after a period of 3 yearsIn Problems 7-14, find the amount that results from each investment. 500 invested at 8 compounded quarterly after a period of 2 1 2 yearsIn Problems 7-14, find the amount that results from each investment. 300 invested at 12 compounded monthly after a period of 1 1 2 yearsIn Problems 7-14, find the amount that results from each investment. 600 invested at 5 compounded daily after a period of 3 yearsIn Problems 7-14, find the amount that results from each investment. 700 invested at 6 compounded daily after a period of 2 yearsIn Problems 7-14, find the amount that results from each investment. 1000 invested at 11 compounded continuously after a period of 2 yearsIn Problems 7-14, find the amount that results from each investment. 400 invested at 7 compounded continuously after a period of 3 yearsIn Problems 15-22, find the principal needed now to get each amount; that is, find the present value. To get 100 after 2 years at 6 compounded monthlyIn Problems 15-22, find the principal needed now to get each amount; that is, find the present value. To got 75 after 3 years at 8 compounded quarterlyIn Problems 15-22, find the principal needed now to get each amount; that is, find the present value. To get 1000 after 2 1 2 years at 6 compounded dailyIn Problems 15-22, find the principal needed now to get each amount; that is, find the present value. To get 800 after 3 1 2 years at 7 compound monthlyIn Problems 15-22, find the principal needed now to get each amount; that is, find the present value. To get 600 after 2 years at 4 compounded quarterlyIn Problems 15-22, find the principal needed now to get each amount; that is, find the present value. To get 300 after 4 years at 3 compounded dailyIn Problems 15-22, find the principal needed now to get each amount; that is, find the present value. To get 80 after 3 1 4 years at 9 compounded continuouslyIn Problems 15-22, find the principal needed now to get each amount; that is, find the present value. To get 800 after 2 1 2 years at 8 compounded continuouslyIn Problems 23—26, find the effective rate of interest. For 5 compounded quarterlyIn Problems 23—26, find the effective rate of interest. For 6 compounded monthlyIn Problems 23—26, find the effective rate of interest. For 5 compounded continuouslyIn Problems 23—26, find the effective rate of interest. For 6 compound continuouslyIn Problems 27-30, determine the rate that represents the better deal. 6 compounded quarterly or 6 1 4 compounded annuallyIn Problems 27-30, determine the rate that represents the better deal. 9 compounded quarterly or 9 1 4 compounded annuallyIn Problems 27-30, determine the rate that represents the better deal. 9 compounded monthly or 8.8 compounded dailyIn Problems 27-30, determine the rate that represents the better deal. 8 compounded semiannually or 7.9 compounded dailyWhat rate of interest compounded annually is required to double an investment in 3 years?What rate of interest compounded annually is required to double an investment in 6 years?What rate of interest compounded annually is required to triple an investment in 5 years?What rate of interest compounded annually is required to triple an investment in 10 years?(a) How long does it take for an investment to double in value if it is invested at 8 compounded monthly? (b) How long does it take if the interest is compounded continuously?(a) How long does it take for an investment to triple in value if it is invested at 6 compounded monthly? (b) How long does it take if the interest is compounded continuously?What rate of interest compounded quarterly will yield an effective interest rate of 7 ?What rate of interest compounded continuously will yield an effective interest rate of 6 ?