Question

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Answer 1

You want to find the time t such that

`\$1000 = \$200 e^(0.04t)`

Divide both sides by $200 :

`(\$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 = (\ln(5))/(0.04) \approx 40.24 \approx \boxed{40}`