#### Problem 64E

64. When you turn on a hot-water faucet, the temperature $T$ of the water depends on how long the water has been running.

(a) Sketch a possible graph of $T$ as a function of the time $t$ that has elapsed since the faucet was turned on.

(b) Describe how the rate of change of $T$ with respect to $t$ varies as $t$ increases.

(c) Sketch a graph of the derivative of $T$.