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 1076: 95

Answer

We would prefer to have $1$ ¢ today, $2$ ¢ tomorrow, $4$ ¢ on day 3, $8$ ¢ on day 4, $16$ ¢ on day 5, and so on, for 30 days.

Work Step by Step

Consider having money in a geometric series for 30 days with ${{a}_{1}}=1$ and $r=2$, and $n=30$. Thus $\begin{align} & {{S}_{n}}=\frac{{{a}_{1}}\left( 1-{{r}^{n}} \right)}{\left( 1-r \right)} \\ & =\frac{1\left( 1-{{2}^{30}} \right)}{\left( 1-2 \right)} \\ & =\frac{1\left( -1073741823 \right)}{\left( 1-2 \right)} \\ & =1,073,741,823 \end{align}$ Which is much greater than the cost of a brand new BMW and 10 million dollars. We we would rather have $1$ ¢ today, $2$ ¢ tomorrow, $4$ ¢ on day 3, $8$ ¢ on day 4, $16$ ¢ on day 5, and so on, for 30 days.
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