Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 4 - Section 4.6 - Modeling with Exponential Functions - 4.6 Exercises - Page 378: 4

Answer

(a) $2298$ (b) $18384$ (c) See graph below.

Work Step by Step

(a) Model the population with an exponential function of base $2$ as $P(t)=P_02^{kt}$ where $P_0$ is the initial population and $k$ is a constant. Since $P(10)=2P_0$, we have $2^{10k}=2$ and get $k=\frac{1}{10}$ At $t=25$, we have $P(25)=P_02^{25/10}=13000$ which gives $P_0=2298$ (b) At $t=5+25=30$, we have $P(30)=2298\times2^{30/10}=18384$ (c) The bird population function can be graphed as shown in the figure.
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