If your allowance was a penny doubled every day, how many days would it take for you to have over $1000? On which day would you have over $10000? How much money would you have on the 15th day?

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- Apr 14th 2009, 06:25 PMlearnmathHELP!!!Word Problem
If your allowance was a penny doubled every day, how many days would it take for you to have over $1000? On which day would you have over $10000? How much money would you have on the 15th day?

- Apr 14th 2009, 06:37 PMtyler.
y = (1+r)^2

y = (1+200%)^2

y = (1+2) ^2

y = 3^2

y = 9

So, on the fifteenth day, you will have $9

This is an example of exponential growth (y = x(1+r)^t where x = initial starting amount, r = rate of growth expressed as a percent and t = time passed under specific unit). Plugging in your other numbvers ($1000 and $10000) as y will give you the answer to the other problems.

****Note that I may be wrong and it may be $6.25. I'm pretty sure that $9 is right, but for some reason my instinct told me to go with 150% the first time I went through with this. Although 150% is NOT doubled. Please check this with your own work or through someone else.**** - Apr 14th 2009, 08:36 PMlearnmath?
The answer is day 18 $1308.16, day 21 $10465.28, on the 15th day $163.52.

I don't know how to calculate this. Please help!!! - Apr 14th 2009, 09:10 PMmr fantastic
Day 1: $0.01

Day 2: $2(0.01)

Day 3: 2(2(0.01)) = $\displaystyle \$ 2^2 (0.01)$

Day 4: $\displaystyle 2 (2^2 (0.01)) = \$ 2^3 (0.01)$

etc.

Day n: $\displaystyle \$ 2^{n-1} (0.01)$.

**Q1**Solve $\displaystyle 2^{n-1} (0.01) > 1000 \Rightarrow 2^{n-1} > 100,000$.

The are many ways of solving this. Using logarithms is one way:

__Spoiler__:

**Q2**Day 15:__Spoiler__: