U.S. Population
YEAR POPULATION
1930 122,800,000
1940 131,700,000
1950 150,700,000
1960 179,300,000
It is estimated that the limiting population that the United Statescan support is 500,000,000 people. Predict the population for theyear 2000 using the logistic growth model on the basis of the datain the years 1930 and 1940. In other words:
* Let P = P (t) be the population, where t is the number of yearsafter 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 thevalues of b and k in the formula for P (t).
Note: Answer to the nearest 1 million people, and do not use commasin your answer.
U.S. Population
YEAR POPULATION
1930 122,800,000
1940 131,700,000
1950 150,700,000
1960 179,300,000
It is estimated that the limiting population that the United Statescan support is 500,000,000 people. Predict the population for theyear 2000 using the logistic growth model on the basis of the datain the years 1930 and 1940. In other words:
* Let P = P (t) be the population, where t is the number of yearsafter 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 thevalues of b and k in the formula for P (t).
Note: Answer to the nearest 1 million people, and do not use commasin your answer.
