A thermometer is removed from a room where the temperature is $70$F and is taken outside, where the air

temperature is $50$F$.$ After one$-$half minute the thermometer reads $65$F$.$ Newton$$s Law of Cooling$/$Warming states:

The rate at which the temperature of a body changes is proportional to the difference between the temperature of the

body and the ambient temperature.

$($a$)$ Write the initial$-$value problem that models T $($t$),$ the temperature of the thermometer at time t$.$

$($b$)$ Find an explicit solution your initial value problem from part $($a$).$

$($c$)$ What is the reading of the thermometer at t $=1$ min?