A thermometer $is$ moved from a room where the temperature $is82Fto$ a freezer where the temperature

$is15F.$ After $30$ seconds the thermometer reads $49F.$ Let $T(t)$ denote the temperature, $in$ Fahrenheit, $at$

time $t,in$ seconds.

$(a)$ Write a differential equation for $T(t).$ The only unknown should $beT(t).$

$T^{\text{'}}(t)=$

$(b)$ What does the thermometer read after $2$ minutes?

$F$

$(c)$ Compute the $limit.$

$\underset{t}{lim}T(t)=$