hi! just needed help on an FRQ for ap calculus ab. let me know if you have any questions for me. I'm just really confused as far as what I am meant to do. If you could walk me through it that would be amazing. THANKS!!

Question

A population is modeled by a function P that satisfies the logistic differential equation. dP/dt = P/5(1-(P/10)).
A. If P(0) = 3, what is lim (as t approaches infinity)P(t)?
B. If P(0) = 20, what is lim (as t approaches infinity)P(t)?
C. A different population is modeled by a function Y that satisfies the seperable differential equation:
dY/dt=(Y/5)(1-(t/10)). Find Y(t) if Y(0) =3.
D. For the function Y found in part (c), what is lim(as t approaches infinity) Y(t)?

Answer 1

well, you should start out by solving the DE:

P = 10/(1+c*e^(-t/5))

(A) P(0) = 3, so
10/(1+c) = 3
c = 7/3

P(t) = 10/(1 + 7/3 e^-t/5)

Now it's clear that P->10

Now try the rest.