Answer
$\approx 140.011$
Work Step by Step
$100\left( 1.02\right) ^{x/4}=200\Rightarrow \left( 1.02\right) ^{x/4}=2\Rightarrow \left( 1.02\right) ^{x}=2^{4}\Rightarrow x=\log _{1.02}2^{4}\approx 140.011$
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