Functions Modeling Change: A Preparation for Calculus, 5th Edition

Published by Wiley
ISBN 10: 1118583191
ISBN 13: 978-1-11858-319-7

Chapter 11 - Polynomial and Rational Functions - 11.1 Power Functions and Proportionality - Exercises and Problems for Section 11.1 - Exercises and Problems - Page 440: 21

Answer

$c=125$ when $d=5$ and $k=5$

Work Step by Step

We are given that $c=45; d=3$ $c$ is directly proportional to $d^2$. We can write $c=kd^2~~~~(1)$ Plug $c=45, d=3$ in equation (1) to obtain: $45=k(3)^2\implies k=5$ Thus, we have: $c=5d^2 ~~~~(2)$ Now, plug $d=5$ in Equation (2) to obtain: $c=5(5)^2 \implies c=125$ Therefore, we get $c=125$ when $d=5$ and $k=5$.
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