Answer
$\dfrac{16 \pi}{9}t^6$
Work Step by Step
We have: $S(r)=4\pi r^2$ and $r(t)=\dfrac{2}{3}t^3$.
Therefore, the composite function will be:
$S(r(t))=4 \pi r^2 \\= 4\pi (\dfrac{2}{3}t^3)^2=\dfrac{16 \pi}{9}t^6$
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Chapter 4 - Exponential and Logarithmic Functions - Section 4.1 Composite Functions - 4.1 Assess Your Understanding - Page 280: 67
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