Barrons AP Calculus - David Bock

14. (a) Solve by separation of variables:

Let c = e−10c; then

Now use initial condition y = 2 at t = 0:

and the other condition, y = 5 at t = 2, gives

(b) Since c = 4 and

Solving for y yields

(c) means 1 + 4 · 2−t = 1.25, so t = 4.

(d) so the value of y approaches 10.