By using Social Security Administration data for selected years from 1950 and projected to 2050, the population of Americans ages 20 to 64 can be modeled by the function

where t is the number of years after 1950 and P(t) is in millions.
(a) Find and interpret P`(45).
(b) At what rate is this population projected to increase in 2040?
(c) What does this tell us about this population after 2040?

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250 -0.0280t 1+1.91e0.0280t P(t)