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: 41

Answer

(a) Linear function: $$V(t) = 0.5t + 2$$ (b) It takes 26 seconds to completely fill the baloon.

Work Step by Step

(a) Linear function: $V(t) = at + b$ Since the rate of change of volume is :$0.5 \space ft^3/s$, a = $0.5$ Since the initial volume is $2 \space ft^3$: $b = 2$ Thus: $$V(t) = 0.5t + 2$$ (b) Solve for $t$, and calculate its value when $V(t) = 15$ $$V(t) - 2 = 0.5t \longrightarrow \frac{V(t) - 2}{0.5} = t$$ $$\frac{15 - 2}{0.5} = t$$ $$t = \frac{13}{0.5} = 26$$
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