Precalculus (6th Edition) Blitzer

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

Chapter 10 - Section 10.3 - Geoetric Sequences and Series - Exercise Set - Page 1075: 70

Answer

a. See table and explanations. b. $a_n=20.85(1.02)^{n-1}$ c. $30.98$ million.
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Work Step by Step

a. See table. The first column is the year, the second column is the population in millions, the third column is the ratio of a population to that of the preceding year, and the last column is the ratio rounded to two decimal places. We can see that Texas has a population increase that is approximately geometric with $r\approx1.02$ (except for the last data point). b. With $a_1=20.85, r=1.02$, we can write the general term as $a_n=20.85(1.02)^{n-1}$, where $n$ is the years after 1999. c. For year 2020, we have $n=2020-1999=21$. Thus, we have $a_{21}=20.85(1.02)^{21-1}\approx30.98$ million.
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