DE: Temperature and Coffee

Problem:

A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 78 °C, it is cooling at a rate of 1°C per minute. When does this occur? Approximate to three decimal places.

Here is my work, please verify if it is correct:

$\displaystyle T(t) = y0 * e^{kt} + Ts$

$\displaystyle 78 = 95*e^{kt}+20$

$\displaystyle 95e^{-t} = 78 - 20$

$\displaystyle

t = - ln(\frac {78 - 20} {95})

$

Therefore, the Coffee's temperature will be decreasing at 1 degree per minute after: 0.4934 minutes.