Use the model below to estimate the average annual growth rate of a certain​ country's population for​ 1950, 1988, and​ 2010, where x is the number of years after 1900.

Question

y=-0.0000087x^3+0.00262x^2-0.174+8.172

The estimated average annual growth rate of the​ country's population for 2010 is

Answer 1

To estimate the average annual growth rate of the country's population for 2010, we need to find the derivative of the given model with respect to x and evaluate it at x = 110 (since 2010 is 110 years after 1900).

Taking the derivative of the model:
dy/dx = -0.0000261x^2 + 0.00524x

Now substituting x = 110 into the derivative:
dy/dx = -0.0000261(110)^2 + 0.00524(110)
= -0.0000261(12100) + 0.5764
= -3.1626 + 0.5764
= -2.5862

The estimated average annual growth rate of the country's population for 2010 is approximately -2.5862.