Answer:
36 days
Step-by-step explanation:
Since the pennies need to be kept under the pillow in order to be doubled, we're really looking for the day the girl will wake up with 21 billions pennies under her pillow.
The general formula of that geometric sequence will be: t = 1 + 2^(n-1)
We need to find the value of n when t will be over 21,000,000,000.
So, the equation becomes:
21,000,000,001 = 1 + 2^(n-1)
2^(n-1) = 21,000,000,000
log(2^(n-1)) = log(21,000,000,000)
(n-1) * log(2) = log(21,000,000,000)
n-1 = log(21,000,000,000) / log(2)
n-1 = 34.29
n = 35.29
Since it has to be complete days, and we have to reach over 21 billions, then we round it up to 36.
