Answer The equation relating the rate of interest (r) and time (t) in years: For investment compounded continuously is given by: t = 109.85 r For investment compounded annually is given by: t = 109.31 r 0.98 Explanation Given information : Annual rate of interest is given by r & time (number of years) is given by t. The completed table for time t (in years) necessary for P dollars to triple when it is invested at an interest rate r compounded continuously is given below: r 2 % 4 % 6 % 8 % 10 % 12 % t (in years) 54.93 27.47 18.31 13.73 10.99 9.16 The completed table for time t (in years) necessary for P dollars to triple when it is invested at an interest rate r compounded annually is given below: r 2 % 4 % 6 % 8 % 10 % 12 % t (in years) 55.48 28.01 18.85 14.27 11.53 9.69 Concept Involved: We need to make us of the below steps to graph the set of data given in the calculator Steps Description Enter the data into the lists. For basic entry of data, see Basic Commands. L 1 _ 2 4 6 8 10 12 | L 2 _ 54.93 27.47 18.31 13.73 10.99 9.16 | L 3 1 _ − − − − − Steps Description Go to STATPLOT (2nd Y=) and choose the first plot. Turn the plot ON, set the icon to Scatter Plot (the first one), set Xlist to L1 and Ylist to L2 (assuming that is where you stored the data), and select a Mark of your choice. S T A T P L O T S 1 : P l o t 1 ... O n L 1 L 2 □ 2 : P l o t 2 ... O f f L 1 L 2 □ 3 : P l o t 3 ... O f f L 1 L 2 □ 4 ↓ P l o t s O f f P l o t 1 P l o t 2 P l o t 3 O n O f f T y p e : X l i s t : L 1 Y l i s t : L 2 M a r k : □ + · Press STAT, arrow right to CALC, and arrow down to A: PwrReg. Hit ENTER. When PwrReg appears on the home screen, type the parameters L1, L2, Y1. The Y1 will put the equation into Y= for you. (Y1 comes from VARS ? YVARS, #Function, Y1) E D I T C A L C T E S T S 6 ↑ C u b i c R e g 7 : Q u a r t R e g 8 : L i n R e g ( a + b x ) 9 : L n R e g 0 : E x p R e g A : P w r R e g B ↓ L o g i s t i c P w r R e g L 1 , L 2 , Y 1 Graph the Power Regression Equation from Y1. ZOOM #9 ZoomStat to see the graph. Graph: Interpretation: The equation relating the rate of interest (r) and time (t) in years for investment compounded continuously is given by: t = 109.85 r The equation relating the rate of interest (r) and time (t) in years for investment compounded annually is given by: t = 109.31 r 0.98

4th Edition

ISBN: 9781337516853

Author: Larson

Publisher: CENGAGE CO

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Question

Chapter 3.5, Problem 18E

To determine

To find : the graph of data found relating the rate of interest and time required for investment to Triple for both compound continuously and annually.

Expert Solution & Answer

Answer to Problem 18E

The equation relating the rate of interest (r) and time (t) in years:

For investment compounded continuously is given by: t=109.85r

For investment compounded annually is given by: t=109.31r0.98

Explanation of Solution

Given information : Annual rate of interest is given by r & time (number of years) is given by t.

The completed table for time t (in years) necessary for P dollars to triple when it is invested at an interest rate r compounded continuously is given below:

r	2%	4%	6%	8%	10%	12%
t (in years)	54.93	27.47	18.31	13.73	10.99	9.16

The completed table for time t (in years) necessary for P dollars to triple when it is invested at an interest rate r compounded annually is given below:

r	2%	4%	6%	8%	10%	12%
t (in years)	55.48	28.01	18.85	14.27	11.53	9.69

Concept Involved:

We need to make us of the below steps to graph the set of data given in the calculator

Steps	Description
Enter the data into the lists. For basic entry of data, see Basic Commands.	L1 _ 24681012\| L 2 _54.9327.4718.3113.7310.999.16\| L 3 1 _ −−−−−

Steps	Description
Go to STATPLOT (2nd Y=) and choose the first plot. Turn the plot ON, set the icon to Scatter Plot (the first one), set Xlist to L1 and Ylist to L2 (assuming that is where you stored the data), and select a Mark of your choice.	STAT PLOTS1: Plot 1...On L1 L2 □2:Plot 2...Off L1 L2 □3:Plot 3...Off L1 L2 □4↓PlotsOff Plot1 Plot2 Plot3 On OffType: Xlist: L1Ylist: L2Mark: □ + ·
Press STAT, arrow right to CALC, and arrow down to A: PwrReg. Hit ENTER. When PwrReg appears on the home screen, type the parameters L1, L2, Y1. The Y1 will put the equation into Y= for you. (Y1 comes from VARS ? YVARS, #Function, Y1)	EDIT CALC TESTS6↑ CubicReg7: QuartReg8:LinReg(a+bx)9:LnReg0:ExpRegA:PwrRegB↓Logistic PwrReg L1, L2, Y1
Graph the Power Regression Equation from Y1. ZOOM #9 ZoomStat to see the graph.

Graph:

EBK PRECALCULUS W/LIMITS, Chapter 3.5, Problem 18E , additional homework tip 1

EBK PRECALCULUS W/LIMITS, Chapter 3.5, Problem 18E , additional homework tip 2

Interpretation:

The equation relating the rate of interest (r) and time (t) in years for investment compounded continuously is given by: t=109.85r

The equation relating the rate of interest (r) and time (t) in years for investment compounded annually is given by: t=109.31r0.98

Chapter 3.5, Problem 17E

Chapter 3.5, Problem 19E

Chapter 3 Solutions

EBK PRECALCULUS W/LIMITS

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