SOLUTION: The types of habitat required for nesting limits the population of a certain species of bird. The population (in billions) behaves according to the “logistic growth” model give

Question 1154017: The types of habitat required for nesting limits the population of a certain species of bird. The population (in billions) behaves according to the “logistic growth” model given by:
P(t) = Ae^(0.01t)/2+e^(0.01t)
where t is the number of years from today and A is a constant.
(a)If the population is 7billion today, how long will it take to
reach 8 billion? Round your final answer to the nearest integer.
b)What eventually happens to the population of this bird species?
Hint: To help simplify the expression consider dividing each
term by something
Answer by greenestamps(13209) (Show Source): You can put this solution on YOUR website!

You show the function as

Clearly that is not a logistic function. Use parentheses where they are required!!

The current population (t=0) in billions is

The function is

(a) Find the number of years until the population reaches 8 billion.

That can be solved algebraically, but it is very tedious. Use a graphing calculator to graph the function itself and the constant 8 and find the intersection. It is at t=20.764 to 3 decimal places.

ANSWER: 21 years, according to the instructions to give the answer as the nearest integer.

(b) What eventually happens to the population?

As t gets large, the "2" in the denominator becomes insignificant; the function approaches

ANSWER: In a long period of time, the limit of the population is 21 billion.

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