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All Textbook Solutions for Precalculus Enhanced with Graphing Utilities

Time Required to Reach a Goal If Tanisha has 100 to invest at 4 per annum compounded monthly, how long will it be before she has 150 ? If the compounding is continuous, how long will it be?Time Required to Reach a Goal If Angela has 100 to invest at 2.5 per annum compounded monthly, how long will it be before she has 175 ? If the compounding is continuous, how long will it be?Time Required to Reach a Goal How many years will it take for an initial investment of 10,000 to grow to 25,000 ? Assume a rate of interest of 6 compounded continuously.Time Required to Reach a Goal how many years will it take for an initial investment of 25,000 to grow to 80,000 ? Assume a rate of interest of 7 compounded continuously.Price Appreciation of Homes What will a 90,000 condominium cost 5 years from now if the price appreciation for condos over that period averages 3 compounded annually?Credit Card Interest A department store charges 1.25 per month on the unpaid balance for customers with charge accounts (interest is compounded monthly). A customer charges 200 and does not pay her bill for 6 months. What is the bill at that time?Saving for a Car Jerome will be buying a used car for 15,000 in 3 years. How much money should he ask his parents for now so that, if he invests it at 5 compounded continuously, he will have enough to buy the car?Paying off a Loan John requires 3000 in 6 months to pay off a loan that has no prepayment privileges. If he has the 3000 now, how much of it should he save in an account paying 3 compounded monthly so that in 6 months he will have exactly 3000 ?Return on a Stock George contemplates the purchase of 100 shares of a stock selling for 15 per share. The stock pays no dividends. Tile history of the stock indicates that it should grow at an annual rate of 15 per year. How much should the 100 shares of stock be worth in 5 years?Return on an Investment A business purchased for 650,000 in 2012 is sold in 2015 for 850,000 . What is the annual rate of return for this investment?Comparing Savings Plans Jim places 1000 in a bank account that pays 5.6 compounded continuously. After 1 year, will he have enough money to buy a computer system that costs 1060 ? If another bank will pay Jim 5.9 compounded monthly, is this a better deal?Savings Plans On January 1, Kim places 1000 in a certificate of deposit that pays 6.8 compounded continuously and matures in 3 months. Then Kim places the 1000 and the interest in a passbook account that pays 5.25 compounded monthly. How much does Kim have in the passbook account on May 1?Comparing IRA Investments Will invests 2000 in his IRA in a bond trust that pays 9 interest compounded semiannually. His friend Henry invests 2000 in his IRA in a certificate of deposit that pays 8 1 2 compounded continuously. Who has more money after 20 years, Will or Henry?Comparing Two Alternatives Suppose that April has access to an investment that will pay 10 interest compounded continuously. Which is better: to be given 1000 now so that she can take advantage of this investment opportunity or to be given 1325 after 3 years?College Costs The average annual cost of college at 4-year private colleges was 31,231 in the 2014-2015 academic year. This was a 3.7 increase from the previous year. Source: The College Board (a) If the cost of college increases by 3.7 each year, what will be the average cost of college at a 4-year private college for the 2034-2035 academic year? (b) College savings plans, such as a 529 plan, allow individuals to put money aside now to help pay for college later. If one such plan offers a rate of 2 compounded continuously, how much should be put in a college savings plan in 2016 to pay for 1 year of the cost of college at a 4-year private college for an incoming freshman in 2034?Analyzing Interest Rates on a Mortgage Colleen and Bill have just purchased a house for 650,000 , with the seller holding a second mortgage of 100,000 . They promise to pay the seller 100,000 plus all accrued interest 5 years from now. The seller offers them three interest options on the second mortgage: (a) Simple interest at 6 per annum (b) 5.5 interest compounded monthly (c) 5.25 interest compounded continuously Which option is best? That is, which results in paying the least interest on the loan?2009 Federal stimulus Package In February 2009, President Obama signed into law a 787 billion federal stimulus package. At that time, 20-year Series EE bonds had a fixed rate of 1.3 compounded semiannually. If the federal government financed the stimulus through EE bonds, how much would it have to pay back in 2029? How much interest was paid to finance the stimulus? Source: U.S. Treasury Department Per Capita Federal Debt In 2015, the federal debt was about 18 trillion. In 2015, the U.S. population was about 320 million. Assuming that the federal debt is increasing about 4.5 per year and the U.S. population is increasing about 0.7 per year, determine the per capita debt (total debt divided by population) in 2030.Inflation Problems 57-62 require the following discussion. Inflation is a term used to describe the erosion of the purchasing power of money. For example, if the annual inflation rate is 3 , then 1000 worth of purchasing power now will have only 970 worth of purchasing power in 1 year because 3 of the original 1000( 0.031000=30 ) has been eroded due to inflation. In general, if the rate of inflation averages r per annum over n years, the amount A that P will purchase after n years is A=P (1r) n where r is expressed as a decimal. Inflation If the inflation rate averages 3 , how much will 1000 purchase in 2 years?Inflation Problems 57-62 require the following discussion. Inflation is a term used to describe the erosion of the purchasing power of money. For example, if the annual inflation rate is 3 , then 1000 worth of purchasing power now will have only 970 worth of purchasing power in 1 year because 3 of the original 1000( 0.031000=30 ) has been eroded due to inflation. In general, if the rate of inflation averages r per annum over n years, the amount A that P will purchase after n years is A=P (1r) n where r is expressed as a decimal. Inflation If the Inflation rate averages 2 , how much will 1000 purchase in 3 years?Inflation Problems 57-62 require the following discussion. Inflation is a term used to describe the erosion of the purchasing power of money. For example, if the annual inflation rate is 3 , then 1000 worth of purchasing power now will have only 970 worth of purchasing power in 1 year because 3 of the original 1000( 0.031000=30 ) has been eroded due to inflation. In general, if the rate of inflation averages r per annum over n years, the amount A that P will purchase after n years is A=P (1r) n where r is expressed as a decimal. Inflation If the amount that 1000 will purchase is only 950 after 2 years, what was the average inflation rate?Inflation Problems 57-62 require the following discussion. Inflation is a term used to describe the erosion of the purchasing power of money. For example, if the annual inflation rate is 3 , then 1000 worth of purchasing power now will have only 970 worth of purchasing power in 1 year because 3 of the original 1000( 0.031000=30 ) has been eroded due to inflation. In general, if the rate of inflation averages r per annum over n years, the amount A that P will purchase after n years is A=P (1r) n where r is expressed as a decimal. Inflation If the amount that 1000 will purchase is only 930 after 2 years, what was the average inflation rate?Inflation Problems 57-62 require the following discussion. Inflation is a term used to describe the erosion of the purchasing power of money. For example, if the annual inflation rate is 3 , then 1000 worth of purchasing power now will have only 970 worth of purchasing power in 1 year because 3 of the original 1000( 0.031000=30 ) has been eroded due to inflation. In general, if the rate of inflation averages r per annum over n years, the amount A that P will purchase after n years is A=P (1r) n where r is expressed as a decimal. Inflation If the average inflation rate is 2 , how long is it until purchasing power is cut in half?Inflation Problems 57-62 require the following discussion. Inflation is a term used to describe the erosion of the purchasing power of money. For example, if the annual inflation rate is 3 , then 1000 worth of purchasing power now will have only 970 worth of purchasing power in 1 year because 3 of the original 1000( 0.031000=30 ) has been eroded due to inflation. In general, if the rate of inflation averages r per annum over n years, the amount A that P will purchase after n years is A=P (1r) n where r is expressed as a decimal. Inflation If the average inflati on rate is 4 , how long is it until purchasing power is cut in half?Problems 63-66 involve zero-coupon bonds. A zero-coupon bond is a bond that is sold now at a discount and will pay its face value at the time when it matures; no interest payments are made. Zero-Coupon Bonds A zero-coupon bond can be redeemed in 20 years for 10,000 . How much should you be willing to pay for it now if you want a return of: (a) 5 compounded monthly? (b) 5 compounded continuously?Problems 63-66 involve zero-coupon bonds. A zero-coupon bond is a bond that is sold now at a discount and will pay its face value at the time when it matures; no interest payments are made. Zero-Coupon Bonds A childâ€™s grandparents are considering buying a 80,000 face-value, zero-coupon bond at birth so that she will have money for her college education 17 years later. If they want a rate of return of 6 compounded annually, what should they pay for the bond?Problems 63-66 involve zero-coupon bonds. A zero-coupon bond is a bond that is sold now at a discount and will pay its face value at the time when it matures; no interest payments are made. Zero-Coupon Bonds How much should a 10,000 face-value, zero-coupon bond, maturing in 10 years, be sold for now if its rate of return is to be 4.5 compounded annually?Problems 63-66 involve zero-coupon bonds. A zero-coupon bond is a bond that is sold now at a discount and will pay its face value at the time when it matures; no interest payments are made. Zero-Coupon Bonds If Pat pays 15,334.65 for a 25,000 face-value, zero-coupon bond that matures in 8 years, what is his annual rate of return?Time to Double or Triple an Investment The formula t= lnm nln( 1+ r n ) can be used to find the number of years t required to multiply an investment m times when r is the per annum interest rate compounded n times a year. (a) How many years will it take to double the value of an IRA that compounds annually at the rate of 6 ? (b) How many years will it take to triple the value of a savings account that compounds quarterly at an annual rate of 5 ? (c) Give a derivation of this formula.Time to Reach an Investment Goal The formula t= lnAlnP r can be used to find the number of years t required for an investment P to grow to a value A when compounded continuously at an annual rate r . (a) How long will it take to increase an initial investment of 1000 to 4500 at an annual rate of 5.75 ? (b) What annual rate is required to increase the value of a 2000 IRA to 30,000 in 35 years? (c) Give a derivation of this formula.Problems 69-72 require the following discussion. The consumer price index (CPI) indicates the relative change in price over time for a fixed basket of goods and services. It is a cost of living index that helps measure the effect of inflation on the cost of goods and services. The CPI uses the base period 1982-1984 for comparison (the CPI for this period is 100). The CPI for March 2015 was 236.12 . This means that 100 in the period 1982-1984 had the same purchasing power as 236.12 in March 2015. In general, if the rate of inflation averages r percent per annum over n years, then the CPI index after n years is CPI=CP I 0 ( 1+ r 100 ) n where CP I 0 is the CPI index at the beginning of the n-year period. Source: U.S. Bureau of Labor Statistics Consumer Price Index (a) The CPI was 214.5 for 2009 and 236.7 for 2014. Assuming that annual inflation remained constant for this time period, determine the average annual inflation rate. (b) Using the inflation rate from part (a), in what year will the CPI reach 300?Problems 69-72 require the following discussion. The consumer price index (CPI) indicates the relative change in price over time for a fixed basket of goods and services. It is a cost of living index that helps measure the effect of inflation on the cost of goods and services. The CPI uses the base period 1982-1984 for comparison (the CPI for this period is 100). The CPI for March 2015 was 236.12 . This means that 100 in the period 1982-1984 had the same purchasing power as 236.12 in March 2015. In general, if the rate of inflation averages r percent per annum over n years, then the CPI index after n years is CPI=CP I 0 ( 1+ r 100 ) n where CP I 0 is the CPI index at the beginning of the n-year period. Source: U.S. Bureau of Labor Statistics Consumer Price Index If the current CPI is 234.2 and the average annual inflation rate is 2.8 , what will be the CPI in 5 years?Problems 69-72 require the following discussion. The consumer price index (CPI) indicates the relative change in price over time for a fixed basket of goods and services. It is a cost of living index that helps measure the effect of inflation on the cost of goods and services. The CPI uses the base period 1982-1984 for comparison (the CPI for this period is 100). The CPI for March 2015 was 236.12 . This means that 100 in the period 1982-1984 had the same purchasing power as 236.12 in March 2015. In general, if the rate of inflation averages r percent per annum over n years, then the CPI index after n years is CPI=CP I 0 ( 1+ r 100 ) n where CP I 0 is the CPI index at the beginning of the n-year period. Source: U.S. Bureau of Labor Statistics Consumer Price Index If the average annual inflation rate is 3.1 , how long will it take for the CPI index to double? (A doubling of the CPI index means purchasing power is cut in half.)Problems 69-72 require the following discussion. The consumer price index (CPI) indicates the relative change in price over time for a fixed basket of goods and services. It is a cost of living index that helps measure the effect of inflation on the cost of goods and services. The CPI uses the base period 1982-1984 for comparison (the CPI for this period is 100). The CPI for March 2015 was 236.12 . This means that 100 in the period 1982-1984 had the same purchasing power as 236.12 in March 2015. In general, if the rate of inflation averages r percent per annum over n years, then the CPI index after n years is CPI=CP I 0 ( 1+ r 100 ) n where CP I 0 is the CPI index at the beginning of the n-year period. Source: U.S. Bureau of Labor Statistics Consumer Price Index The base period for the CPI changed in 1998. Under the previous weight and item structure, the CPI for 1995 was 456.5 . If the average annual inflation rate was 5.57 , what year was used as the base period for the CPI?Explain in your own words what the term compound interest means. What does continuous compounding mean?Explain in your own words the meaning of present value.Critical Thinking You have just contracted to buy a house and will seek financing in the amount of 100,000 . You go to several banks. Bank 1 will lend you 100,000 at the rate of 4.125 amortized over 30 years with a loan origination fee of 0.45 . Bank 2 will lend you 100,000 at the rate of 3.375 amortized over 15 years with a loan origination fee of 0.95 . Bank 3 will lend you 100,000 at the rate of 4.25 amortized over 30 years with no loan origination fee. Bank 4 will lend you 100,000 at the rate of 3.625 amortized over 15 years with no loan origination fee. Which loan would you take? Why? Be sure to have sound reasons for your choice. Use the information in the table to assist you. If the amount of the monthly payment does not matter to you, which loan would you take? Again, have sound reasons for your choice. Compare your final decision with others in the class. Discuss.1AYU 2AYU 3AYU 4AYU 5AYU 6AYU 7AYU 8AYU 9AYU 10AYU 11AYU 12AYU 13AYU 14AYU 15AYU 16AYU 17AYU 18AYU 19AYU 20AYU 21AYU 22AYU 23AYU 24AYU 25AYU 26AYU 27AYU 28AYU 29AYU 1AYU 2AYU 3AYU 4AYU 5AYU 6AYU 7AYU 8AYU 9AYU 10AYU 11AYU 12AYU 13AYU 1RE 2RE 3RE 4RE 5RE 6RE 7RE 8RE 9RE 10RE 11RE 12RE 13RE 14RE 15RE 16RE 17RE 18RE 19RE 20RE 21RE 22RE 23RE 24RE 25RE 26RE 27RE 28RE 29RE 30RE 31RE 32RE 33RE 34RE 35RE 36RE 37RE 38RE 39RE 40RE 41RE 42RE 43RE 44RE 45RE 46RE 47RE 48RE 49RE 50RE 51RE 52RE 53RE 54RE 55RE 1CT 2CT 3CT 4CT 5CT 6CT 7CT 8CT 9CT 10CT 11CT 12CT 13CT 14CT 15CT 16CT 17CT 18CT 19CT 20CT 21CT 22CT 23CT 24CT 25CT 26CT 27CT 28CT 29CT 1CR 2CR 3CR 4CR 5CR 6CR 7CR 8CR 9CR 10CR 11CR 12CR 13CR 14CR 15CR What is the formula for the circumference C of a circle of radius r ? What is the formula for the area A of a circle of radius r ? (p. A16)If an object has a speed of r feet per second and travels a distance d (in feet) in time t (in seconds), then d= _____ . (pp. A69-A71)An angle is in _____ _____ if its vertex is at the origin of a rectangular coordinate system and its initial side coincides with the positive x-axis .A _____ _____ is a positive angle whose vertex is at the Center of a circle.If the radius of a circle is r and the length of the arc subtended by a central angle is also r , then the measure of the angle is 1 _____ . a. degree. b. minute. c. second. d. radian.On a circle of radius r , a central angle of radians subtends an arc of length s= _____; the area of the sector formed by this angle is A= _____ .180 = _____ radians a. 2 b. c. 3 2 d. 2 An object travels on a circle of radius r with constant speed. If s is the distance traveled in time t on the circle and is the central angle (in radians) swept out in time t , then the linear speed of the object is v= _____ and the angular speed of the object is = _____ .True or False The angular speed of an object traveling on a circle of radius r is the angle (measured in radians) swept out, divided by the elapsed time t .True or False For circular motion on a circle of radius r , linear speed equals angular speed divided by r .In Problems 11-22, draw each angle in standard position. 30 In Problems 11-22, draw each angle in standard position. 60 In Problems 11-22, draw each angle in standard position. 135 In Problems 11-22, draw each angle in standard position. 120 In Problems 11-22, draw each angle in standard position. 450 In Problems 11-22, draw each angle in standard position. 540 In Problems 11-22, draw each angle in standard position. 3 4 In Problems 11-22, draw each angle in standard position. 4 3 In Problems 11-22, draw each angle in standard position. 6 In Problems 11-22, draw each angle in standard position. 2 3 In Problems 11-22, draw each angle in standard position. 16 3 In Problems 11-22, draw each angle in standard position. 21 4 In Problems 59-64, convert each angle to a decimal in degrees. Round your answer to two decimal places. 40 1025 In Problems 59-64, convert each angle to a decimal in degrees. Round your answer to two decimal places. 61 4221 25AYU 26AYU In Problems 59-64, convert each angle to a decimal in degrees. Round your answer to two decimal places. 9 99 28AYU In Problems 65-70, convert each angle to DMS form. Round your answer to the nearest second. 40.32 In Problems 65-70, convert each angle to DMS form. Round your answer to the nearest second. 61.24 In Problems 65-70, convert each angle to DMS form. Round your answer to the nearest second. 18.255 In Problems 65-70, convert each angle to DMS form. Round your answer to the nearest second. 29.411 In Problems 65-70, convert each angle to DMS form. Round your answer to the nearest second. 19.99 In Problems 65-70, convert each angle to DMS form. Round your answer to the nearest second. 44.01 In Problems 23-34, convert each angle in degrees to radians. Express your answer as a multiple of . 30 In Problems 23-34, convert each angle in degrees to radians. Express your answer as a multiple of . 120 In Problems 23-34, convert each angle in degrees to radians. Express your answer as a multiple of . 240 In Problems 23-34, convert each angle in degrees to radians. Express your answer as a multiple of . 330 In Problems 23-34, convert each angle in degrees to radians. Express your answer as a multiple of . 60 In Problems 23-34, convert each angle in degrees to radians. Express your answer as a multiple of . 30 In Problems 23-34, convert each angle in degrees to radians. Express your answer as a multiple of . 180 In Problems 23-34, convert each angle in degrees to radians. Express your answer as a multiple of . 270 In Problems 23-34, convert each angle in degrees to radians. Express your answer as a multiple of . 135 In Problems 23-34, convert each angle in degrees to radians. Express your answer as a multiple of . 225 In Problems 23-34, convert each angle in degrees to radians. Express your answer as a multiple of . 90 In Problems 23-34, convert each angle in degrees to radians. Express your answer as a multiple of . 180 In Problems 35â€”46, convert each angle in radians to degrees. 3 In Problems 35â€”46, convert each angle in radians to degrees. 5 6 In Problems 35â€”46, convert each angle in radians to degrees. 5 4 In Problems 35â€”46, convert each angle in radians to degrees. 2 3 In Problems 35â€”46, convert each angle in radians to degrees. 2 In Problems 35â€”46, convert each angle in radians to degrees. 4 In Problems 35â€”46, convert each angle in radians to degrees. 12 In Problems 35â€”46, convert each angle in radians to degrees. 5 12 In Problems 35â€”46, convert each angle in radians to degrees. 2 In Problems 35â€”46, convert each angle in radians to degrees.In Problems 35â€”46, convert each angle in radians to degrees. 6 In Problems 35â€”46, convert each angle in radians to degrees. 3 4 In Problems 47-52, convert each angle in degrees to radians. Express your answer in decimal form, rounded to two decimal places. 17 In Problems 47-52, convert each angle in degrees to radians. Express your answer in decimal form, rounded to two decimal places. 73 In Problems 47-52, convert each angle in degrees to radians. Express your answer in decimal form, rounded to two decimal places. 40 In Problems 47-52, convert each angle in degrees to radians. Express your answer in decimal form, rounded to two decimal places. 51 In Problems 47-52, convert each angle in degrees to radians. Express your answer in decimal form, rounded to two decimal places. 125 In Problems 47-52, convert each angle in degrees to radians. Express your answer in decimal form, rounded to two decimal places. 350 In Problems 53-58, convert each angle in radians to degrees. Express your answer in decimal form, rounded to two decimal places. 3.14 In Problems 53-58, convert each angle in radians to degrees. Express your answer in decimal form, rounded to two decimal places. 0.75 In Problems 53-58, convert each angle in radians to degrees. Express your answer in decimal form, rounded to two decimal places. 2 In Problems 53-58, convert each angle in radians to degrees. Express your answer in decimal form, rounded to two decimal places. 3 In Problems 53-58, convert each angle in radians to degrees. Express your answer in decimal form, rounded to two decimal places. 6.32 In Problems 53-58, convert each angle in radians to degrees. Express your answer in decimal form, rounded to two decimal places. 2 In Problems 71-78, s denotes the length of the are of a circle of radius r subtended by the central angle . Find the missing quantity. Round answers to three decimal places. r=10meters , = 1 2 radian , s= ?In Problems 71-78, s denotes the length of the are of a circle of radius r subtended by the central angle . Find the missing quantity. Round answers to three decimal places. r=6feet , =2radians , s= ?In Problems 71-78, s denotes the length of the are of a circle of radius r subtended by the central angle . Find the missing quantity. Round answers to three decimal places. = 1 3 radian , s=2feet , r= ?In Problems 71-78, s denotes the length of the are of a circle of radius r subtended by the central angle . Find the missing quantity. Round answers to three decimal places. = 1 4 radian , s=6centimeters , r= ?In Problems 71-78, s denotes the length of the are of a circle of radius r subtended by the central angle . Find the missing quantity. Round answers to three decimal places. r=5miles , s=3miles , = ?In Problems 71-78, s denotes the length of the are of a circle of radius r subtended by the central angle . Find the missing quantity. Round answers to three decimal places. r=6meters , s=8meters , = ?In Problems 71-78, s denotes the length of the are of a circle of radius r subtended by the central angle . Find the missing quantity. Round answers to three decimal places. r=2inches , =30 , s= ?In Problems 71-78, s denotes the length of the are of a circle of radius r subtended by the central angle . Find the missing quantity. Round answers to three decimal places. r=3meters , =120 , s= ?In Problems 79-86, A denotes the area of the sector of a circle of radius r formed by the central angle . Find the missing quantity. Round answers to three decimal places. r=10meters , = 1 2 radian , A= ?In Problems 79-86, A denotes the area of the sector of a circle of radius r formed by the central angle . Find the missing quantity. Round answers to three decimal places. r=6feet , =2radians , A= ?In Problems 79-86, A denotes the area of the sector of a circle of radius r formed by the central angle . Find the missing quantity. Round answers to three decimal places. = 1 3 radian , A=2squarefeet , r= ?In Problems 79-86, A denotes the area of the sector of a circle of radius r formed by the central angle . Find the missing quantity. Round answers to three decimal places. = 1 4 radian , A=6squarecentimeters , r= ?In Problems 79-86, A denotes the area of the sector of a circle of radius r formed by the central angle . Find the missing quantity. Round answers to three decimal places. r=5miles , A=3squaremiles , = ?In Problems 79-86, A denotes the area of the sector of a circle of radius r formed by the central angle . Find the missing quantity. Round answers to three decimal places. r=6meters , A=8squaremeters , = ?In Problems 79-86, A denotes the area of the sector of a circle of radius r formed by the central angle . Find the missing quantity. Round answers to three decimal places. r=2inches , =30 , A= ?In Problems 79-86, A denotes the area of the sector of a circle of radius r formed by the central angle . Find the missing quantity. Round answers to three decimal places. r=3meters , =120 , A= ?87AYU 88AYU 89AYU 90AYU 91AYU 92AYU 93AYU 94AYU 95AYU 96AYU 97AYU 98AYU 99AYU 100AYU 101AYU 102AYU 103AYU 104AYU 105AYU 106AYU 107AYU 108AYU 109AYU 110AYU 111AYU 112AYU 113AYU 114AYU 115AYU 116AYU 117AYU 118AYU 119AYU 120AYU 121AYU 122AYU

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