U.S. Population It is estimated that the limiting population that the United Sta

Question

U.S. Population

It is estimated that the limiting population that the United States can support is 500,000,000 people. Predict the population for the year 2000 using the logistic growth model on the basis of the data in the years 1930 and 1940. In other words:

Let P = P (t) be the population, where t is the number of years after 1930.

Assume P (t) is of the form given by the logistic equation. Determine what the value of L must be in this case.

Find the exact values of P (0) and P (10) from the U.S. Population table given above. Use these two data points to find the values of b and k in the formula for P (t).

Note: Answer to the nearest 1 million people, and do not use commas in your answer.

Explanation / Answer

The logistic model formula for the population,

Here, , , then

Let , the year is 1940, then

Therefore, the logistic model form is,

To predict the population for the year 2000, need to find at .

Now,

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