word problem with expotintial

[john m]

I heard a word problem today and can not for the life of me remember the area of math it would be associated with or the formula to work it.
For 1 month (31) days I give you one cent the first day. Then it doubles the second day and doubles each day till the end of the month. How much would you have at the end of the month?
I worked it out the long way on a calculator but it is driving me nuts that I can not remember the math. Please, help an old man stay, well, relatively sane.

 

[stapel]

The numbers -- 1, 2, 4, 8, 16, etc -- are doubling. This sequence of numbers is called a "geometric" sequence. The total value at the end of the period would be the "sum" of the geometric "series". You'd use the formula for that sum.

 

[Ishuda]

I heard a word problem today and can not for the life of me remember the area of math it would be associated with or the formula to work it.
For 1 month (31) days I give you one cent the first day. Then it doubles the second day and doubles each day till the end of the month. How much would you have at the end of the month?
I worked it out the long way on a calculator but it is driving me nuts that I can not remember the math. Please, help an old man stay, well, relatively sane.

Another way to say it is
G(d) = 2 G(d-1)
= 2 (2 G(d-2) ) = 2² G(d-2)
= 2² (2 G(d-3) ) = 2³ G(d-3)
= ... = 2^d-2 G(2)
= 2^d-2 (2 G(1) ) = 2^d-1 G(1)
or
G(d) = $0.01 * 2^d-1

But now you need to add them up as mentioned previously.