Question: Let W be the amount of water, in gallons, in a bathtub at time t, in minutes.
(a) What are the meaning and units of dW/dt?
(b) Suppose the bathtub is full of water at time t0, so that W(t0) > 0. Subsequently, at time tp > t0, the plug is pulled. Is dW/dt positive, negative, or zero:
(i) For t0 p?
(ii) After the plug is pulled, but before the tub is empty?
(iii) When all the water has drained from the tub?