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?
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.****
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: