The number of customers, n, of a food shop t months after it opens for the first time can be modelled as a continuous variable. It is suggested that the number of customers increasing at a rate that is proportional to the square root of n.

a. Form and solve a differential equation relating n and t to model this information.

b. Initially, n = 0, and after 6 months the food shop has 3600 customers. Find how many complete months it takes for the number of customers to reach 6800.

c. The food shop has a capacity of serving 14 000 customers per month. Show that the model predicts  shop will have reached its capacity sometime in the 12th month.