Question 59232: Lyn and her friends made a pile of 31 snowballs this morning. Then the sun came out. It melted 1 snowball in the first hour, 2 snowballs in the second hour; and 4 snowballs in the third hour. Each hour the sun is melting twice as many snowballs as it did the hour before. If the sun keeps melting snowballs in this way, how many hours in all will it take the sun to melt the whole pile of snowballs?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Lyn and her friends made a pile of 31 snowballs this morning. Then the sun came out. It melted 1 snowball in the first hour, 2 snowballs in the second hour; and 4 snowballs in the third hour. Each hour the sun is melting twice as many snowballs as it did the hour before. If the sun keeps melting snowballs in this way, how many hours in all will it take the sun to melt the whole pile of snowballs?
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If you know geometric series you may recognize the following:
S(n)=a[r^(n+1)-1]/(r-1)
For your problem a=1,r=2, S(n)=31, and you are looking for "n".
31=1[2^(n+1)-1]/(2-1)
31=2^(n+1) - 1
2^(n+1)=32
2^(n+1)=2^5
n+1=5
n=4
It will take 4 days to melt the 31 snowballs.
Cheers,
Stan H.
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