Could someone answer this so I understand it. Thanks

Question

The projected rate of increase in enrollment at a new college is estemated by

dE/dt = 9000(t+1)^-3/2
where E(t) is the projected enrollment in t years. If the enrollment is 5000 now (t=0), find the projected enrollment 35 years from now.

Round to the nearest integer as needed.

Answer 1

from dE/dt we can find E(t)

E(t) = -18000(t+1)^(-1/2) + c
when t=0, E(0) = 5000
5000 = -18000(1)^(-1/2) + c
c = 23000

E(t) = -18000(1+t)^(-1/2) + 23000
e(35) = -18000(36)^(-1/2) + 23000
= -18000/√36 + 23000
= 20000

Answer 2

-13500 not 18000