Consider a $42^\circ$F object placed in $65^\circ$F room.

(a) Write a differential equation for $H$, the temperature of the object at time $t$, using $k>0$ for the constant of proportionality, and write your equation in terms of $H$, $k$, and $t$.
$H' =$

(b) Give the general solution for your differential equation. Simplify your solution in terms of an unspecified constant $C$, which appears as the coefficient of an exponential term, and the growth factor $k$.
$H =$
(Your answer may involve the constant of proportionality $k$.)

(c) The temperature of the object is $42^\circ$F initially, and $48^\circ$F one hour later. Find the temperature of the object after $5$ hours.
$H(5) =$ degrees F