Question

a magic penny under a girfs pillow. The next night there are 2 magic pennies under her pillow. The following morning she linds four pennies of pennies seen under the pillow each day is the grand total, that is, the Apparently, while she sleeps each penny turns into two magic pennies. The total pennies from each of the previous days are not being stored away days This course (Math 1332 CUVO1 Spring 2019) is based on Bennett: Using and

Answer 1

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, 32....

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,

S_n = { a × ( rⁿ - 1 ) } ÷ ( r - 1 )

where,

a = initial term = 1,

r = common ratio = 2,

S_n = $175 billion = $175 × 10⁹ = 175 × 10¹¹ pennies

Putting values in the formula we get

175 × 10¹¹ = { 1 × (2ⁿ - 1 ) } ÷ ( 2-1)

2ⁿ = 175×10¹¹ + 1

Taking log of both sides, we get

n × log(2) = log(175 × 10¹¹ + 1)

n = 44 days