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After n years of 7 percent growth, the value is (1.07)n times the starting value.

The answer to the question is the smallest value of n such that (1.07)n >=2

or nlog(1.07)>= log(2)

or n >= log(2)/log(1.07) = 10.2

So the GDP will double during the 11th year.

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Q: If the growth rate is 7 percent how many years will it take for the GDP to double?
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