Solve the Problem $\mathrm { y } = 550 \mathrm { t } + 27,500 + 37,500 \mathrm { e } ^ { - .02 \mathrm { t } }$

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) = 11t.

A) $\mathrm { y } = 550 \mathrm { t } + 27,500 + 37,500 \mathrm { e } ^ { - .02 \mathrm { t } }$
B) $y = 550 \mathrm { t } - 27,500 + 37,500 \mathrm { e } ^ { - .02 \mathrm { t } }$
C) $y = - 550 t - 27,500 + 37,500 e ^ { - .02 t }$
D) $y = - 550 \mathrm { t } - 27,500 + 37,500 \mathrm { e }^{ \cdot 02 \mathrm { t }}$