Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Review - Exercises - Page 167: 41

Answer

(a) $f'(r)$ is the instantaneous rate of change of the total cost of repaying the loan at an interest rate of $r$ The units of $f'(r)$ are $\$/(percent~per~year)$ (b) $f'(10) = 1200$ means that at an interest rate of 10% per year, the total cost of the loan is increasing at a rate of $\$1200/(percent~per~year)$ (c) $f'(r)$ is always positive.

Work Step by Step

(a) The interest rate is $r$% per year The total cost of repaying a student loan is $C = f(r)$ $f'(r)$ is the instantaneous rate of change of the total cost of repaying the loan at an interest rate of $r$ The units of $f'(r)$ are $\$/(percent~per~year)$ (b) Let's suppose that the interest rate $r$ is increasing. $f'(10) = 1200$ means that when the interest rate reaches 10% per year, the total cost of the loan is increasing at a rate of $\$1200/(percent~per~year)$ (c) Since a higher interest rate always results in a higher total cost to repay the loan, $f'(r)$ is always positive.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.