The table gives the U.S. population to the nearest million (actual or projected)

Question

The table gives the U.S. population to the nearest million (actual or projected) for selected years. (a) Find a cubic function P(t) that models these data, where P is the U.S. population in millions and t is the number of years past 1960. (Round your coefficients to three significant figures.) P(t)= (b)Find the function that models the instantaneous rate of change of the U.S. population. P?(t)= (c) Find the instantaneous rates of change in 2000 and 2025. (Round your answers to two decimal places.) 2000 2025

Explanation / Answer

a)

(-7.285 * 10^-5)*t^3 + (1.385 * 10^-2)*t^2 + 1.980t + 1.826 * 10^2

b)

Deriving :

(-2.186 * 10^-4)*t^2 + (2.770 * 10^-2)*t + 1.980

c)

In 2000, t = 40
So, plug that into the equation in B above.....
2.74 ---> ANSWER

In 2025, t = 65 :
So, plug in t = 65 into B :
2.86 ---> ANSWER

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