I did this problem already but want to make sure my steps are correct, please show all work/explanations

1) a island has a population of 20,000 birds. A disease starts where 10 birds have gotten infected, and 4 days later, 200 birds are infected. the rate at which the disease spreads is proportional to the number of birds infected and the quotient of the number of birds not yet infected and the population of the island.

(I know, The quotient of a and b is ab but am struggling at this part a bit)

a) Find an equation for the number of birds infected at time t (t in days).

b) how many birds are infected two weeks into the disease