Question

A leprechaun places a magic penny under a​ girl's pillow. The next night there are 2 magic pennies under her pillow. The following morning she finds four pennies.​ Apparently, while she sleeps each penny turns into two magic pennies. The total number of pennies seen under the pillow each day is the grand​ total; that​ is, 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 351 billion​?

Answer 1

Answer:

Given that:

A leprechaun places a magic penny under a​ girl's pillow. The next night there are 2 magic pennies under her pillow. The following morning she finds four pennies.​

Apparently, while she sleeps each penny turns into two magic pennies.

day 1 = 1 pennies = $0.01

Day 2 = 2 pennies = $ 0.02

Day 3 = 4 pennies = $ 0.08

Each day the pennies are getting douload.

It is a geometric sequence having first term , a = 0.01

Common ratio , r = 2

let n = no .of days.

Sum of n terms or total money $ 351 billion.

Take log on both side