Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 2 - Section 2.7 - Combining Functions - 2.7 Exercises - Page 218: 79

Answer

$f(t)=16\pi t^2$ Where $f(t)$ represents surface are, for given $t$ time (in seconds).

Work Step by Step

We know the formula for surface area of a sphere: $A=4\pi r^2$ Let's say that $f(t)$ is the surface area of the balloon. To formulate the function, we have to express the radius in terms of $t$. The radius expands by $2cm$ every second, so the radius is : $r= 2t$ Now we can write: $f(t)=4\pi(2t)^2=16\pi t^2$
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