$[10pts.]$

The temperature $of$ I. Newton's cup $of$ coffee decreases $at$ a rate that $is$

proportional $to$ the difference between the temperature $of$ the coffee $(T)$ and the

temperature $of$ the room, which $is$ currently $73$ degrees Fahrenheit.

$(a)$ Write the differential equation $to$ describe this situation and use the separation

$of$ variables technique $to$ find the model $T(m)$ that gives Newton's coffee

temperature $at$ minute $m.$