Question

Use algebra to solve the following equation. Round decimal to two places.20 = 95 • e^-0.03t

Answer 1

`20=95\cdot e^(-0.03t)`

Dividing by 95 at both sides of the equation:

`\begin{gathered} (20)/(95)=(95\cdot e^(-0.03t))/(95) \\ (4)/(19)=e^(-0.03t) \end{gathered}`

Taking natural logarithm at both sides of the equation:

`\begin{gathered} \ln ((4)/(19))=\ln (e^(-0.03t)) \\ \ln ((4)/(19))=-0.03t\cdot\ln (e^{}) \\ \ln ((4)/(19))=-0.03t \end{gathered}`

Dividing by -0.03 at both sides of the equation:

`\begin{gathered} (\ln ((4)/(19)))/(-0.03)=(-0.03t)/(-0.03) \\ (\ln((4)/(19)))/(-0.03)=t \\ 51.94\approx t \end{gathered}`