Solve the Problem $y = - 400 t - 20,000 - 10,000 \mathrm { e } \cdot 02 \mathrm { t }$

Multiple Choice

Solve the problem.
-dy/dt = ky + f(t) is a population model where y is the population at time t and f(t) is some function to describe the net effect on the population. Assume k = .02 and y = 10,000 when t = 0. Solve the differential equation of y
When f(t) = -8t.

A) $y = - 400 t - 20,000 - 10,000 \mathrm { e } \cdot 02 \mathrm { t }$
B) $y = - 400 t + 20,000 - 10,000 \mathrm { e } ^ { - .02 t }$
C) $y = 400 t + 20,000 - 10,000 e ^ { - .02 t }$
D) $y = 400 t + 20,000 - 10,000 \mathrm { e } ^{\cdot 02 \mathrm { t }}$