Let N be the number of years after which GDP will be equal in both countries. Then
$18 trillion x (1.02)N = $9 trillion x (1.07)N
[(1.07)N] / [(1.02)N] = $18 trillion / $ trillion
[(1.07 / 1.02)N] = 2
(1.0490)N = 2
Taking natural logarithm on both sides,
N x ln 1.0490 = ln 2
N x 0.0478 = 0.6931
N = 14.5 years
Therefore, China will surpass US after 14.5 years, i.e. in year 15.
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