Question

if someone offers to pay you 1 penny on the first day, 2 pennies on the second day, 4 pennies on the third day, 8 pennies on the fourth day, 16 pennies on the fifth day ad so on. What is the first day on which your pay would be at least $100.

Answer 1

The pay on the nth day is 2^(n-1)
So,we want

2^(n-1) = 10000
n-1 = log10000/log2
n = 14.28

So, on the 15th day the pay is 2^14 = $163.84