College Algebra (6th Edition)

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

Chapter 8 - Summary, Review, and Test - Review Exercises - Page 790: 56

Answer

$9,333,333$

Work Step by Step

The total spending can be represented by the sum of the infinite geometric series with first term $a_1=4,000,000\cdot0.7=2800000$ and common ratio $r=0.7$. An infinite geometric series converges if and only if $|r|\lt1$, where $r$ is the common ratio. If it converges, then it equals $\frac{a_1}{1-r}$ where $a_1$ is the first term. Here $0.7\lt1$. Hence the sum: $\dfrac{2800000}{1-0.7}=9,333,333$
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