Question

500= 100e^(0.04t)

A. t= 25ln(5)
B. t= 25log(5)
C. t= 25ln(400)
D. t= 25log(400)

Answer 1

A.
`t=25\ln(5)`

Explanation:

We want to solve for t in
`500=100e^(0.04t)`

Divide through by 100

`5=e^(0.04t)`

Take natural logarithm of both sides

`\ln(5)=\ln(e^(0.04t))`

This simplifies to:
`\ln(5)=0.04t`

Divide both sides by 0.04

`(\ln(5))/(0.04)=t`

`t=25\ln(5)`