Question

one model of earths population growth is $p(t)=\frac{64}{(1 + 11e^{-0.08t})}$, where t is measured in years since 1990, and p is measured in billions of people. which of the following statements are true? check all that apply. a. the carrying capacity of earth is 64 billion people. b. the population of earth is increasing by a steady rate of 8% per year. c. in 1990, there were 5.33 billion people. d. the population of earth will grow exponentially without bound.

Explanation:

Step1: Analyze carrying capacity

The logistic model is $P(t)=\frac{K}{1+Ae^{-rt}}$, where $K$ is carrying capacity. Here $K=64$, so A is true.

Step2: Check growth rate type

Logistic growth is not steady exponential (8% steady rate is exponential), so B is false.

Step3: Calculate 1990 population

1990 is $t=0$: $P(0)=\frac{64}{1+11e^0}=\frac{64}{12}\approx5.33$, so C is true.

Step4: Check unbounded growth

Logistic growth approaches $K$, not unbounded, so D is false.

Answer:

A. The carrying capacity of Earth is 64 billion people, C. In 1990, there were 5.33 billion people.