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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Future Value In Exercises 79 and 80, find the future value of the income (in dollars) given by f(t) over t 1

years at annual interest rate r. If the function f represents a continuous investment over a period of t, years at an annual interest rate r (in decimal form) compounded continuously, then the future value of the investment is given by

Future value = e n , 0 t f ( t ) e r t d t . .

f ( t ) = 3000 e 0.05 t , r = 10 %     t 1 = 5  years

To determine

To calculate: The future value if model f(t)=3000e0.05t for time period of 5 years and annual interest rate is 10% by using the provided equation.

Explanation

Given information:

Interest rate is 10% for the time period of 5 years.

The provided expression is:

Future value=ert10t1f(t)ertdt

Formula used:

t1t2ertdt=ert2rert1r

Calculation:

Consider the expression for future value is,

Future value=ert10t1f(t)ertdt

Where r is interest rate and t1 is time period.

Here the Interest rate that is,

r=10%=0.1

The time period that is t1=5 years and f(t)=3000e0.05t.

Now substitute all the values in the future formula as:

Future value=e(0

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