Functions Modeling Change: A Preparation for Calculus, 5th Edition

Published by Wiley
ISBN 10: 1118583191
ISBN 13: 978-1-11858-319-7

Chapter 4 - Exponential Functions - 4.1 Introduction to the Family of Exponential Functions - Exercises and Problems for Section 4.1 - Exercises and Problems - Page 145: 4


Yes, $m(t)=8 \cdot 27^t$

Work Step by Step

Since $(ab)^n=a^nb^n$, this function simplifies to $$m(t)=2^3 \cdot (3^t)^3$$ Using the fact that $(a^b)^c=a^{bc}$, $(3^t)^3=3^{3t}=(3^3)^t=27^t$. This leaves an exponential function of $$m(t)=8 \cdot 27^t$$
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