Question

Finding the time given an exponential function with base e that models a real-world situation

Answer 1

We are solving for the value of t if C(t) = 19. We can rewrite the equation into

`19=5+17e^(-0.038t)`

Solving for t, we have

`\begin{gathered} 17e^(-0.038t)=19-5 \\ 17e^(-0.038t)=14 \\ e^(-0.038t)=(14)/(17) \\ -0.038t=\ln (14)/(17) \\ -0.038t=-0.1941 \\ t=(-0.1941)/(-0.038) \\ t\approx5.1 \end{gathered}`

The bottled water will achieve a temperature of 19 degrees C after 5.1 minutes.

Answer: 5.1 min