Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.2 Mathematical Models: A Catalog of Essential Functions - 1.2 Exercises - Page 34: 19


(a) $y = \frac{4.34}{10}x + 15$ (b) $196$ ft

Work Step by Step

(a) At 0 ft of descent (ie. the surface), the water pressure is $15$ $lb/in^{2}$. Thus, that is the y-intercept for the graph of water pressure as a function of depth below the ocean surface, or $b$. For every 10 ft, the water pressure increases by $4.34$ $lb/in^{2}$, so $m$ must be such that when $x$ is 10, $mx$ is $4.34$. Thus, $m= \frac{4.34}{10}$. The function is then: $y = \frac{4.34}{10}x + 15$ (b) When the pressure is $100$ $lb/in^{2}$, $y = 100$. Inputting this into the equation gives: $100 = \frac{4.34}{10}x +15$ $85 = \frac{4.34}{10}x$ $85 \div \frac{4.34}{10} = x$ $x \approx 196$ ft
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