You want to find the time t such that
[tex]\$1000 = \$200 e^{0.04t}[/tex]
Divide both sides by $200 :
[tex]\dfrac{\$1000}{\$200} = 5 = e^{0.04t}[/tex]
Take the logarithm of both sides:
[tex]\ln(5) = \ln(e^{0.04t}) = 0.04t\ln(e) = 0.04t[/tex]
Divide both sides by 0.04 and solve for t :
[tex]t = \dfrac{\ln(5)}{0.04} \approx 40.24 \approx \boxed{40}[/tex]
