Calculus: Early Transcendentals 8th Edition

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

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


(a) The function is $p=15+0.434d$ where $p$ is in lb/in$^2$ and $d$ is in feet. (b) The depth is $195.85$ feet.

Work Step by Step

(a) This function is linear. The pressure starts from $15$ lb/in$^2$ and increases by $4.34$ lb/in$^2$ for every ten feet of descend. If we measure the depth $d$ in feet we would have that the pressure increases for $4.34/10=0.434$ for every foot of descend: $$p=15 + 0.434d.$$ (b) We will put $100$ lb/in$^2$ for pressure into the equation from part (a): $$100=15+0.434d\Rightarrow 0.434d=100-15=85$$ and this gives $$d=\frac{85}{0.434} = 195.85$$ in feet.
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