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 = -0.000009x^3 + 0.0025x^2 - 0.201x + 7.979

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

Answer 1

To estimate the average annual growth rate of a certain country's population for 2010 using the given model, we need to find the derivative of the model function with respect to x. The derivative will give us the rate of change of the population over time.

Taking the derivative of the model function y = -0.000009x^3 + 0.0025x^2 - 0.201x + 7.979, we get:

dy/dx = -0.000027x^2 + 0.005x - 0.201

To estimate the average annual growth rate for 2010 (which is 110 years after 1900), we substitute x = 110 into the derivative:

dy/dx = -0.000027(110)^2 + 0.005(110) - 0.201

Simplifying this equation will give us the estimated average annual growth rate for 2010.