Answer
$1250$
Work Step by Step
Consider the exponential growth as: $y=y_0e^{kt}$
As we are given that $y(3)=10,000$ and $y(5)=40,000$
Then, we have $10,000=y_0 e^{3k}$ and $40,000=y_0 e^{5k}$
From the above two equations, we get $y_0 e^{5k}=4y_0 e^{3k}$
or, $e^{2k}=4$ or, $k= \ln 2$
$y=y_0e^{(\ln 2)t} \implies 10,000=(y_0) e^{3 \ln 2}$
or, $10,000=y_0e^{\ln (2^3)}$
so, $10,000=(8) y_0 \implies y_0=1250$
