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.
y=-0.0000087x^3 + 0.00262x^2 - 0.174x + 8.172
The estimated average annual growth rate of the country's population for 1950 is ____
To estimate the average annual growth rate for 1950, we need to find the value of y when x is equal to 50 (since 1950 is 50 years after 1900).
y = -0.0000087(50^3) + 0.00262(50^2) - 0.174(50) + 8.172
Calculating this equation will give us the estimated average annual growth rate for 1950.
To find the estimated average annual growth rate of the country's population for 1950, we need to calculate the derivative of the given function with respect to x.
Taking the derivative of y = -0.0000087x^3 + 0.00262x^2 - 0.174x + 8.172:
dy/dx = (-0.0000087 * 3)x^2 + (0.00262 * 2)x - 0.174
Simplifying the equation:
dy/dx = -0.0000261x^2 + 0.00524x - 0.174
To find the average annual growth rate, we substitute x = 1950 into the derivative equation:
dy/dx = -0.0000261(1950)^2 + 0.00524(1950) - 0.174
Calculating this expression will give us the estimated average annual growth rate for 1950.