A hard$-$boiled egg is removed from a pot of water and set on the counter to cool. Initially, the egg$$s temperature is

$180$oF$.$ After an hour, its temperature is $140$oF$.$ The temperature of the room is $70$oF$.$

Assume that Newton$$s Law of Cooling$/$Warming applies: The rate of cooling$/$warming is proportional to the

difference between the current temperature and the ambient temperature.

$($a$)$ Write an initial$-$value problem that models the temperature of the egg. Let T represent the current temperature

of the egg at time, t$,$ in hours.