Question 1190095: Topics In Contemporary Math
Exponential Growth
2) Which would you rather have, one million dollars or the amount of money you would get
if a penny was doubled every day for a (30-day) month?
Found 3 solutions by math_tutor2020, ikleyn, Alan3354:
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
The sequence of penny amounts is:
1,2,4,8,...
which is a geometric sequence with the following properties
a = 1 = first term
r = 2 = common ratio
Compute the sum of the first n = 30 terms to get
Sn = a*(1-r^n)/(1-r)
S30 = 1*(1-2^30)/(1-2)
S30 = 1,073,741,823
Over the course of 30 days, you would get 1,073,741,823 pennies
This converts to (1,073,741,823)/100 = $10,737,418.23 which is 10.7 million dollars approximately
Answer by ikleyn(52879)  (Show Source):
You can put this solution on YOUR website! .
Notice that the geometric progression
1, 2, 4, 8, 16, . . .
with the first term 1 and the common ratio 2 has very simple formula for the sum
of the first n terms  = 
(surely, it is a particular case of the general formula . . . )
It facilitates calculations - - - so, it is useful and worth to be MEMORIZED,
in addition to the general formula.
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! Which would you rather have, one million dollars or the amount of money you would get if a penny was doubled every day for a (30-day) month?
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"if a penny was doubled" is not clear. There's no way to double a penny.
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If you receive a penny the 1st day, then 2 pennies the 2nd day, that's 3 pennies.
Day Pennies
1 1
2 3
3 7
4 15
5 31
6 63
If that's the case, in 30 days you have 2^30-1 = 1,073,741,823 pennies.
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If the total amount is doubled each day, then you have 2 pennies the 2nd day, not 3. In 30 days you have 2^29 pennies = 536,870,912 pennies.
Day Pennies
1 1
2 2
3 4
4 8
5 16
6 32
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