Corpororate administration notice that 13 % of their employees retire each year. while 2,500 are newely hired. What is the long-term effect if they initianly have 30,000 employees.

Question

Corpororate administration notice that 13 % of their employees retire each year. while 2,500 are newely hired. What is the long-term effect if they initianly have 30,000 employees.

I found the function:
DE/dt=-.13E+2500
Where do I go from here?

Answer 1

solve the DE to get

E(t) = c*e^(-.13E) + 19230.8
E(0) = 30000 = c*1 + 19230.8
c = 10769.2

E(t) = 10769.2e^(-.13E) + 19230.8

while the hiring rate remains constant, the retirement rate falls off as the workforce decreases. In the long run, the workforce will stabilize near 19230.