Question

One model of Earth's population growth is P(t)= 64/(1+11e^0.8t)
where t is
measured in years since 1990, and P is measured in years since 1990, and Pis measured in billions of people. Which of the following statements are true? Check all that apply.

Answer 1

Answer: C and D

Step-by-step explanation:

Answer 2

Using the logistic equation, it is found that options C and D are correct.

The logistic equation for population growth is given by:

$P(t) = \frac{K}{1 + Ae^{-kt}}$

$A = \frac{K - P(0)}{P(0)}$

In which:  

• K is the carrying capacity.

• P(0) is the initial value.

• k is the growth rate, as a decimal.

• The population grows exponentially for a while, but as it gets closer to the carrying capacity, the growth slows down.

For this problem, the equation is:

$P(t) = \frac{64}{1 + 11e^{-0.08t}}$

Which means that:

• The carrying capacity is of 64 billion people, as $K = 64$.

• The growth rate is of 8% per year, but it is not steady.

• The initial population, in millions of people, is of $P(0) = \frac{64}{1 + 11} = 5.3$.

Hence, options C and D are correct.

To learn more about the logistic equation, you can check https://brainly.com/question/25697660