very awkward question....?

Question

A conservation society introduced a herd of buffalo into a game preserve. The growth of the herd was modeled by the logistics curve:

P(t) = (450) / (1+8e^(-0.489t))

(a)According to the model, how many animals were introduced initially?

(b)According to the model, what is the limit to the size of the herd?

Answer 1

P(t) = (450) / (1+8e^(-0.489t))

According to the model, how many animals were introduced initially
At initial t = 0
:>animals were introduced initially = 450/9
=50

According to the model, what is the limit to the size of the herd
P(t) = (450) / (1+8e^(-0.489t))
differentiate P(t) in terms of t and then find t.
Replace the value of t in the equation.

Answer 2

(a) At time t=0, P(0) = 450 / (1+ 8e^0) = 50.

(b) They plan for this herd to grow until it reaches a limit. Take time = infinity as your limit. Then

P(inf) = 450 / (1 + 8e^(minus infinity)) = 450 / (1 + 0) = 450.

Answer 3

Question a)
P(0) = 450 / (1 + 8)
P(0) = 50
50 were introduced initially.

Question b)
P(t) = 450 / (1 + 8.e^(- 0.489 t))
P(t) = 450 / [ 1 + 8 / e^(0.489 t) ]
As t--> ∞ , P-->450
Limit to size of herd = 450

Answer 4

(a)
At time = 0, e^(-0.489t) = e^(-0) =1/1
Therefore, P(0) = 450 / (1 + 8/1) = 50.

(b)
At time = infinity, e^(-0.489t) = e^(-infinity) = 1/infinity.
Therefore, P(infinity)= 450 / (1 + 8/infinity)
= 450 / (1 + 0) = 450 / 1
= 450.