Suppose that the amount of water contained in a plant at time t is denoted by V(t). Due to evaporation, V(t) changes over time. Suppose that the change in volume at time t, measured over a 24-hour period, is proportional to t (24 - t), measured in grams per hour. To offset the water loss, you water the plant at a constant rate of 4 grams of water per hour. (a) Explain why for some positive constant a, describes this situation. (b) Determine the constant a for which the net water loss over a 24-hour period is equal to 0.

dV dt = : at (24 t) + 4