1. a researcher firm finds that the average number of customers that are in Somerset Mall on a
Saturday varies sinusoidally with time. The mall is open from 9:00 am to 9:00 pm; the minimum number of customers is at 9:00 am and 9:00 pm when there are zero customers. The maximum
number of customers is at 3:00 pm when there are 875 customers in the mall.

a) Sketch and label this situation. [3pts.]

b) Write an equation to represent this relationship where y represents the number of customers in
the mall and x represents the number of hours past 9:00 am. Note: The domain of this function will be
[0, 12]. [5pts.)

c) On a particular Saturday, the mall decides to have a prize for the 500th customer to arrive.
Determine at what time the prize will be given. [3pts.]