Question

A leprechaun place is a Magic penny under a girls pillow the next night there are two magic pennies under the pillow the following morning she finds four pennies While She Sleeps each Penny turns into to magic pennies the total number of pennies seen under the pillow each day is the grand total that’s it the pennies from each of the previous days are not being stored away until more pennies magically appear how many days would elapse before she has a total of more than two $687 million. 

Answer 1

Answer:

37 days

Step-by-step explanation:

I assume the total we need is $687 million. I don't know what "two $687 million" means.

Day 1: 1 penny = 2^0 pennies = $0.00

Day 2: 2 pennies = 2^1 pennies = $0.02

Day 3: 4 pennies = 2^2 pennies = $0.04

Day 4: 8 pennies = 2^3 pennies = $0.08

Day x: $687,000,000 = 68,700,000,000 pennies = 2^(x - 1)

$2^{x - 1} = 68,700,000,000$

$\log (2^{x - 1}) = \log (68,700,000,000)$

$(x - 1) \log 2 = \log (68,700,000,000)$

$x \log 2 - \log 2 =  \log (68,700,000,000)$

$x \log 2 = \log (68,700,000,000) + \log 2$

$x = \dfrac{\log (68,700,000,000) + \log 2}{\log 2}$

$x = 37$

Answer: 37 days