SOLUTION: Algebra 1 problem using powers and exponents. Someone offers to double the amount of money you have every day for 1 month (30 days). You have 1 nickel. On the first day, you wil

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Question 707283: Algebra 1 problem using powers and exponents.
Someone offers to double the amount of money you have every day for 1 month (30 days). You have 1 nickel. On the first day, you will have 2 nickels worth $.10. On the second day, you will have 4 nickels worth $.20. How much money will you have on the 30th day?
Answer by jsmallt9(3759) About Me  (Show Source):
You can put this solution on YOUR website!
This is essentially an exponential growth/decay problem. A general equation for these is:
A+=+A%5B0%5D%2Ar%5Et
where
t = number of units of time
A = the amount after t units of time
A%5B0%5D = the initial amount (IOW: The amount at t = 0)
r = the factor of change for 1 unit of time. If r > 1 then the equation is for growth and if 0 < r < 1 then the equation is for decay.

In your problem:
n = 30 days
r = 2 (since the amount doubles each day)
A%5B0%5D = 0.05
So your equation is:
A+=+0.05%2A2%5E30
Finding 2%5E30:
A+=+0.05%2A1073741824
Multiplying:
A+=+53687091.2
So after 30 days you will have $53,687,091.20 (Close to $54 million dollars!!)