SOLUTION: A sum of money doubles itself in 10 years. The number of years it would triple itself is?

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Question 1209369: A sum of money doubles itself in 10 years. The number of years it would triple itself is?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Let a be the initial amount; let r be the growth factor each year. Then, since the amount doubles in 10 years,

a%28r%5E10%29=2a
r%5E10=2a%2Fa=2
r=root%2810%2C2%29 = 1.07177 to several decimal places.

We want to find the number of years n it takes the amount to triple:

a%28r%5En%29=3a
r%5En=3

The variable is in an exponent, so use logarithms.

n%2Alog%28r%29=log%283%29
n=log%283%29%2Flog%28r%29 = 15.85 to two decimal places

ANSWER: approximately 15.85 years

Of course, if we want an answer in whole numbers of years we need to round that up to 16 years.