Adisease is spreading through a herd of 200 goats. let g(t) be the number of goats who have the disease t days after the outbreak. the disease is spreading at a rate proportional to the number of goats who do not have the disease. suppose that 20 goats had the disease initially and 50 goats have the disease after 2 weeks.

(a) give the mathematical model (initial-value problem) for g.
(b) find the general solution of the differential equation in (a).
(c) find the particular solution that satisfies the given conditions.