Question

In: Advanced Math

Assume the carrying capacity of the earth is 15 billion. Use the 1960s peak annual growth...

Assume the carrying capacity of the earth is

15

billion. Use the 1960s peak annual growth rate of

2.1​%

and population of

3

billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of

6.8

billion. How does the predicted growth rate compare to the actual growth rate of about

1.2​%

per​ year?

What is the base growth​ rate?

Assume the carrying capacity of the earth is

15

billion. Use the 1960s peak annual growth rate of

2.1​%

and population of

3

billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of

6.8

billion. How does the predicted growth rate compare to the actual growth rate of about

1.2​%

per​ year?

What is the base growth​ rate?

Assume the carrying capacity of the earth is

15

billion. Use the 1960s peak annual growth rate of

2.1​%

and population of

3

billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of

6.8

billion. How does the predicted growth rate compare to the actual growth rate of about

1.2​%

per​ year?

What is the base growth​ rate?

Assume the carrying capacity of the earth is

15

billion. Use the 1960s peak annual growth rate of

2.1​%

and population of

3

billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of

6.8

billion. How does the predicted growth rate compare to the actual growth rate of about

1.2​%

per​ year?

What is the base growth​ rate?

Assume the carrying capacity of the earth is

15

billion. Use the 1960s peak annual growth rate of

2.1​%

and population of

3

billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of

6.8

billion. How does the predicted growth rate compare to the actual growth rate of about

1.2​%

per​ year?

What is the base growth​ rate?

Assume the carrying capacity of the earth is

15

billion. Use the 1960s peak annual growth rate of

2.1​%

and population of

3

billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of

6.8

billion. How does the predicted growth rate compare to the actual growth rate of about

1.2​%

per​ year?

What is the base growth​ rate?

Assume the carrying capacity of the earth is

15

billion. Use the 1960s peak annual growth rate of

2.1​%

and population of

3

billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of

6.8

billion. How does the predicted growth rate compare to the actual growth rate of about

1.2​%

per​ year?

What is the base growth​ rate?

Solutions

Expert Solution

Assume the carrying capacity of the earth is 15 billion. Use the 1960s peak annual growth rate of 2.1​% and population of 3 billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of 6.8 billion. How does the predicted growth rate compare to the actual growth rate of about 1.2​% per​ year? What is the base growth​ rate?

We suppose in the logistic model that the population, in billions, is given by the expression

where is the number of years after . Here is the carrying capacity, 15 billion. Then

.

We have that is the population in , 3 billion. Therrefore and

.

We have


.

Then, and

.

The population now (2020) is given by


.

The model overestimates the population.

As for the population, the model also overestimates the growth rate.

The base growth rate is .

Colby Messinger answered 3 years ago
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