Question

MTH/21ST:Quantitative Reasoning Homework: Week 4 Homework Score: 0 of 1 p Mw Score: 2955%, 65of22pts 8 A.23 a whole number มาม.iernth' arewer box andren cic. Check Anisor Gateway

a leprechun 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 $703 billion?

Answer 1

At the beginning there was 1 penny. At the second day the amount of pennies under the pillow became 2. The amount of pennies doubled each day. So the series is, 1, 2, 4, 8, 16,3.. This series is in geometric progression. As the pennies from each of the previous days are not being stored away until more pennies magically appear so the sum of series will be, Sn (ax (rn-1)-(r-1) where, a initial term 1, r= common ratio = 2, Sn $703 billion $703 x 109 703 x 1011 pennies Putting values in the formula we get 703 x 1011 1x (2n -1))(2-1) 2n 703x10111 Taking log of both sides, we get n x log(2) log(703 x 1011+1) n 46 days