College Algebra (6th Edition)

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

Chapter 8 - Sequences, Induction, and Probability - Exercise Set 8.3 - Page 742: 95

Answer

Second option.

Work Step by Step

The total amount of money in the second case is the sum of the geometric series with first term $a_1=0.01$, common ratio $r=2$ from $i=1$ to $i=30$. The sum of a geometric sequence until $n$ can be obtained by the formula $S_n=a_1(\frac{1-r^n}{1-r})$ where $a_1$ is the first term and $r$ is the common ratio. Hence here the sum if: $S_n=0.01(\frac{1-2}{1-2^{30}})=10737418.23\gt1000000$. thus I would choose the second option.
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