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: 77

Answer

(a) $g(t)=60t$ (b) $f(r)=\pi r^2$ (c) $f∘g=3600\pi t^2$ This simply represents the area of circle for given $t$ seconds.

Work Step by Step

(a) According to the information we are given, every $t$ second the circular ripple travels $60cm$, so we can simply write a function to model the radius of this circle for given $t$ second. $g(t)=60t$ Where $g(x)$ represents radius in $cm$ and $t$ time in $sec$. (b) As we found out previously in (a) radius for given $t$ sec is $60t$. (Which we will need to calculate area of the circle for any given time). In general Area of circle is equal to $\pi r^2$, so we can write: $f(r)=\pi r^2$ (c) $f∘g=f(g(t))=f(60t)=\pi \times (60t)^2=3600\pi t^2$ $f∘g=3600\pi t^2$ This simply represents the area of circle for given $t$ seconds.
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