(D) If Q is the concentration at time t, then . We separate
variables and integrate:
We let Q(0) = Q 0 . Then
We now find t when Q = 0.1Q 0 :
(E) See Case III: Logistic Growth in Chapter 9 for the characteristics of
the logistic model.
(D) (A), (B), (C), and (E) are all of the form y′ = ky(a − y).
(B) The rate of growth, , is greatest when its derivative is 0 and the
curve of is concave down. Since
therefore
which is equal to 0 if , or 500, animals. The curve of y′ is concave
down for all P, since
so P = 500 is the maximum population.
