Question

Solving Exponential and Logarithmic Equation In exercise,solve for x or t.See example 5 and 6.

400e - 0.0174t = 1000

Answer 1

The solution is
`t = -52.66`

Explanation:

The first step to solve this equation is placing everything with the exponential to one side of the equality, and everything without the exponential to the other side. So

`400e^(-0.0174t) = 1000`

`e^(-0.0174t) = (1000)/(400)`

`e^(-0.0174t) = 2.5`

The ln is the interse operation to the exponential, so we apply the ln to both sides of the equality.

`\ln{e^(-0.0174t)} = ln(2.5)`

`-0.0174t = 0.9163`

`t = -(0.9163)/(0.0174)`

`t = -52.66`