Question

??????????????????????????????

Answer 1

You want to find the time t such that

$\ 1000 = \ 200 e^{0.04t}$

Divide both sides by $200 :

$\dfrac{\ 1000}{\ 200} = 5 = e^{0.04t}$

Take the logarithm of both sides:

$\ln(5) = \ln(e^{0.04t}) = 0.04t\ln(e) = 0.04t$

Divide both sides by 0.04 and solve for t :

$t = \dfrac{\ln(5)}{0.04} \approx 40.24 \approx \boxed{40}$