By using Social Security Administration data for selected years from 1950 and projected to 2050, the U.S.

Question:

By using Social Security Administration data for selected years from 1950 and projected to 2050, the U.S. population, ages 20-64, P (in millions) can be approximated by the equation

where t is the number of years past 1950.
(a) Some of the Social Security Administration data for this population (in millions) are as follows.

For each of these years, use the equation to find the predicted U.S. population, ages 20-64.
(b) From 2000 to 2020, this population group is predicted to change by 28.4 million individuals. Find the population change predicted by the equation for 2025 to 2045. Is this greater or less than 2000-2020?
(c) Why is it reasonable for a formula such as this to have an upper limit that cannot be exceeded? Use large t-values to discover this formula's upper limit.