A thermometer is moved from a room where the temperature is $81$F to a freezer where the temperature is $12$F$.$ After $30$ seconds the thermometer reads $53$F$.$ 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 be T$($t$).$

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

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

$$F

$($c$)$ Compute the limit$.$

limt$$T$($t$)=$