#### Answer

This occurs after 20.3 minutes.

#### Work Step by Step

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.