A student has set up a new coffee shop in campus in January. The shop only sells medium coffee, and the price of a cup does not vary by ingredients added. In the first month (January), the student sold 72,000 coffee cups. The sales of coffee increase by 1800 cups every month after the first month (i.e., from February onwards). Given the hard economic times, the student also decided to increase the price of coffee each month at an equal rate

The price of coffee (p) is a function time in months (t) and is represented by the function: () = 1.50 + 0.003², where t = 0 for the month of January

a) Find the monthly revenue function (a formula for the monthly revenue), and then compute its rate of change at the beginning of April. (6 points)

b) The number of students who purchase coffee in a month is given by n(t) = 1200 + 0.4t, where t is in months, just like in part a). Find a formula for the average number of coffee cups each student buys in a month [C(t)], and estimate the rate at which this number was growing at the beginning of March.

c) On average, how many cups of coffee did each student purchase in the month of January. How many cups of coffee per day does this translate to? (3 Points)