please solve this question

3. A health clinic has set up a flu shot program for its patients. The clinic is open from 8 am to 4 pm (16:00) and gives flu shots on a first-come, first-serve basis. The clinic has the capacity to serve 30 patients per hour. The function r(t), whose graph is given below, gives the rate at which people are arriving at the clinic for shots one day. r(t) (people/hr) 45- 30 15 9 10 11 12 13 14 15 16 t (time) Explain your answers to the questions below by relating them to points, lengths, or areas on the graph. (a) If someone arrives at 9 AM, how long do they have to wait for a shot? (b) At what time does a line start forming? (c) At approximately what time is the length of the line increasing most rapidly? (d) At approximately what time is the line the longest? (The answers to this is different from the answer to (c); explain why.) (e) When the line is longest, approximately how many people are in line? (f) Approximate the longest amount of time a person could wait for a shot. (Assume that doors close to new arrivals at 4 pm but everyone who has arrived by 4 pm is served.) (g) Approximately how long is the line at 3 pm? (h) Approximate the number of people who came to the clinic for a flu shot this day