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

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

Chapter 5 - Logarithmic Functions - Strengthen Your Understanding - Page 228: 5



Work Step by Step

Use the fact that $e^{\ln b}=b$ for all positive $b$ to convert the equation into $$y=a(e^{\ln b})^t$$ Next, use the identity that $(a^b)^n=a^{bn}$ to simplify the equation to $$y=ae^{t \ln b}$$ This means that $k$ must be equal to $\ln b$ in the form $y=ae^{kt}$. This makes the statement true.
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