The logistic growth function P(t)= 160/ 1 + 9e^-0.165t describes the population of the endangered species of elk "t" years after

Question

a. How many elk were initially introduced into the habitat?
b. How many elk are expected after 6 years?
What is the limited size of elk population sustained by the habitat?

Answer 1

Hi Brianna,

 

To solve parts a) and b), you just need to plug in appropriate values for the time t.

 

a. When a problem refers to an "initial" condition, that means when time t = 0.

P(0) = 160/(1+9*e⁰)

 

b. In this case, it asks about time t = 6,

P(6) = 160/(1+9*e^(-0.165*6))

In both cases, you should be able to calculate these on your calculator without too much difficulty.

 

The final question asks about the maximum sustainable size of the population. With a logistic growth function, this is simply the ratio of the constants in the numerator and denominator. In this particular case, that is

160/1 = 160