A leprechaun places a magic penny under a girl\'s pillow. The next night there a

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 $175 billion( proceed by trial and error)

Explanation / Answer

Here, the pennies are increasing exponentially as

After t days the amount would become = $0.01 * 2t

There to become $175 billion,

$175,000,000,000 = $0.01 * 2t

2t = 175,000,000,000 / 0.01 = 17,500,000,000,000

t ln 2 = ln 17,500,000,000,000

t = 30.49/ln2

t = 30.49 / 0.6931

t = 43.98 which is approximatly 44 days

Therefore around 44days would elapse before she has a total of more than $175 billion.

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