College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.5 - Page 505: 35


a. $ 1\%$ b. 69 years

Work Step by Step

Exponential growth model: $A=A_{0}e^{kt} \qquad(k>0)$ ($A_{0}$ is the initial quantity, $A$ is the quantity after time t). ----------- a. Reading k directly from the model $A=4.3e^{0.01t},$ $k=0.01$, ( New Zealand's growth rate is $ 1\%$) $\mathrm{b}$. Using the given formula for doubling time, $ t=\displaystyle \frac{\ln 2}{0.01}\approx$69.314718056 To the nearest whole year: 69 years.
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