Another model for a growth function for a limited population is given by the Gompertz function, which is a solution to the diffe
rential equation dPdt=cln(KP)P where c is a constant and K is the carrying capacity. Answer the following questions.
a. Solve the differential equation with a constant c=0.1, carrying capacity K=3000, and initial population P0=1000. Answer: P(t)=
(b) Compute the limiting value of the size of the population. limt→[infinity]P(t)= .(c) At what value of P does P grow fastest? P= .
a. Solve the differential equation with a constant c=0.1, carrying capacity K=3000, and initial population P0=1000. Answer: P(t)=
(b) Compute the limiting value of the size of the population. limt→[infinity]P(t)= .(c) At what value of P does P grow fastest? P= .
1 answer:
You might be interested in
The order in which gifts are received doesn't matter - if child X gets toy 1 then toy 2, it's the same as giving child X toy 2 then toy 1 - so we are counting combinations.
The eldest child receives 3 of the 7 gifts, so they have
possible choices of gifts.
The next child receives 2 of the remaining 4 gifts, so they have
choices.
The last child receives the remaining 2 gifts, and there is only
way to select the gifts for them.
By the multiplication using, the total number of ways of distributing 7 gifts among 3 children in the prescribed way is 35 • 6 • 1 = 210.