SOLUTION: Sam deposits 100 dollars in his account on Tuesday. If he doubles the amount he deposits every day, what is the equation that will determine how much is in his account?
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Question 1061781: Sam deposits 100 dollars in his account on Tuesday. If he doubles the amount he deposits every day, what is the equation that will determine how much is in his account? Answer by addingup(3677) (Show Source):
You can put this solution on YOUR website! Second day: 200
first day: 100
So we have a series with a ratio of 200/100 = 2
Now, the sum of a geometric series S with n terms and with a ratio r is:
S = (first term)(1-r^n)/(1-r)
Since we have a first term 100 and a ratio of 2, to find the sum after n days we do this:
= 100(1-2^n)/(1-2)
-.-.-.-.-.-.-.-.
Let's test this formula. Let's say that he's been saving for 4 days:
100(1-2^4)/(1-2) = 1,500
Compare with this:
Day 1 = 200-100 = 100
Day 2 = 400-100 = 300
Day 3 = 800-100 = 700
Day 4 = 1600-100 = 1500
So our formula works.
