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 ​$2 billion​?

Answer 1

ANSWER:
Day 1 => i pronny = $0.00 Daya=> 2 pernice - $4002 Day 3>) 14 Pennies $004 Dayu+ 8 Pennies - $0.08. Sach day the permis are getting doubled. .: It is a geometsic._sequence having Piret term a=001 common ralio 8:2 Let n = no of days .. Sum of n terms of total money 2 $2 billion · af 19.]> 2000000000 ou (>200 000 24> 200000000000 2"> 20000000000 Take log' on both sides 10g(20) > log(200000000001)

In logo > log (200000000001) m> log (200000000001) Log 2. ns. 10.30lo 0.3 0102 m> 3428 m = 34 days