Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 3 - Section 3.5 - Exponential Growth and Decay; Modeling Data - Exercise Set - Page 505: 10


$334.7$ million

Work Step by Step

Exponential growth model $: \quad A= A_{0}e^{kt}$. If $ k \gt 0$, the function models the amount of a growing entity. $ A_{0}$ is the original amount, or size, of the growing entity at time t = 0, $ A $ is the amount at time $ t $, and $ k $ is a constant representing the growth rate. If k is negative, the model is an exponential decay model. ---- Model: $ A=A_{0}e^{kt}$ $ t=0$ for the year $2010.$ Unknown: $ A $, when $ A_{0}=184.4, t=40, k=0.0149$ $ A=184.4e^{0.0149\cdot 40}\approx 334.7$ million
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