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 - 4.5 The Number e - Exercises and Problems for Section 4.5 - Exercises and Problems - Page 173: 24

Answer

The population of City A is growing faster than City B.

Work Step by Step

Since the population of City A is growing by a constant continuous percent rate, the function can be modelled as an exponential function. Let $a= P_0$ and $b= 0.15$ $$ P=P_0 e^{0.15 t}=P_0\left(e^{0.15}\right)^t=P_0(1.1618)^t $$ From this, we see that $b= 1.1618$. The population increases by about $16.18\%$ per year. Hence, the population of City A is growing faster than City B.
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