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ljb402 · Nov 27, 2011, 04:14 PM

Mary's parents decided to give her an allowance every Saturday. The first Saturday they gave her $.01. For each successive week, they double the amount given the previous week. If Mary saves her allowance, in how many weeks will she become a millionaire?

ebaines · Nov 28, 2011, 11:45 AM

If you approach this using pennies, then $1 miilion = 100,000,000 pennies.

The amount of pennies received each week is $P_i = 2^i$ , where i=0 for week 1, i=1 for week 2, etc. The sum of all pennies received in week i plus all previous weeks is:

$ P_{total} = \Sigma P_i = 2^{(i+1)} -1$ .

So for the first few weeks you get:

$ \begin{matrix} Week\ i & P_t\\ ------ & ----- \\ 0 & 1 \\ 1 & 3 \\ 2 & 7 \\ 3 & 15 \\ 4 & 31 \\ \end{matrix} $

etc.

To determine when she will be a millionaire you need to solve for $i$ :

$ 2^{(i+1)} -1 = 100,000,000 $

Do you know how to solve for i?