A hot brick is removed from a kiln at $150^{\circ}$C above room temperature. Over time, the brick cools off. After 2 hours have elapsed, the brick is $20^{\circ}$C above room temperature. Let $t$ be the time in hours since the brick was removed from the kiln. Let $y=H(t)$ be the difference between the brick's and the room's temperature at time $t$. Assume that $H(t)$ is an exponential function.

(a) Find a formula for $H(t)$.
$H(t) =$ .

(b) How many degrees does the brick's temperature drop during the first quarter hour?
It drops $^{\circ}$ C.

(c) How many degrees does the temperature drop during the next quarter hour?
It drops $^{\circ}$ C.

(d) Find $H^{-1}(y)$.
$H^{-1}(y) =$ .

(e) How much time elapses before the brick's temperature is $3^{\circ}$C above room temperature?
time = hours.