Alejandro plans to begin filling his backyard pool with water at noon. Assume noon represents t = 0 for time t in minutes. The depth of water in the pool is the product of the rate at which the water flows into the pool and time. The total depth of the water when the pool is full is 120 centimeters.
a. Alejandro begins filling his pool 15 minutes later than planned. Write the function relating the time since noon to the rate r at which water flows into the pool. Graph the function.
b. Analyze the key features of the graph in the context of the situation.