Calculus 8th Edition

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

Chapter 1 - Functions and Limits - 1.3 New Functions from Old Functions - 1.3 Exercises - Page 44: 56


(a)$$r=2t$$ (b)$$(V \circ r)(t)= \frac{32}{3} \pi t^3$$ This composite function represents the volume of the inflating spherical balloon in terms of time.

Work Step by Step

(a) The value of the radius of the inflating spherical balloon equals the velocity times the elapsed time. So we have $$r=2t.$$ (b)$$V=\frac{4}{3} \pi r^3$$ $$\Rightarrow \quad (V \circ r)(t)=V(r(t))=\frac{32}{3} \pi t^3$$
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