U$.$S$.$ Population

YEAR POPULATION

$1930122,800,000$

$1940131,700,000$

$1950150,700,000$

$1960179,300,000$

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$).$