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.

Step-by-step explanation:

Given that a  disease 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) i.e.

Initially

b)

c) G(2) =50

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.