Chapter 3 - Section 3.8 - Exponential Growth and Decay - 3.8 Exercises - Page 246: 18

This occurs after 20.3 minutes.

We can find $k$: $\frac{dT}{dt} = k(T-20)$ $k(70-20) = -1$ $k = \frac{-1}{50}$ $k = -0.02$ We can find $t$: $T(t) = 20+75~e^{kt} = 70$ $75~e^{kt} = 50$ $e^{kt} = \frac{50}{75}$ $kt = ln(\frac{2}{3})$ $t = \frac{ln(\frac{2}{3})}{k}$ $t = \frac{ln(\frac{2}{3})}{-0.02}$ $t = 20.3~min$ This occurs after 20.3 minutes.