Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Section 2.5 - Linear Functions and Models - 2.5 Exercises - Page 196: 42

Answer

$(a) V(t) = 10t + 300$ $(b)$ It takes 100 minutes to completely fill the pond.

Work Step by Step

(a) Linear function: $V(t) = at + b$ Since the rate of change of volume is :$10 \space gal/min$, a = $10$ Since the initial volume is $300 \space gal$: $b = 300$ Thus: $$V(t) = 10t + 300$$ (b) Solve for $t$, and calculate its value when $V(t) = 1300$ $$V(t) - 300 = 10t \longrightarrow \frac{V(t) - 300}{10} = t$$ $$\frac{1300 - 300}{10} = t$$ $$t = \frac{1000}{10} = 100$$
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