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= -0.0000088x^3+0.00214x^2-0.202+7.906
The estimated average annual growth rate of the country's population for 1950 is
To estimate the average annual growth rate of the country's population for 1950, we need to substitute x = 50 into the equation:
y = -0.0000088(50^3) + 0.00214(50^2) - 0.202(50) + 7.906
Calculating this expression gives us:
y ≈ -0.0000088(125000) + 0.00214(2500) - 0.202(50) + 7.906
y ≈ -1.1 + 5.35 - 10.1 + 7.906
y ≈ 1.156
Therefore, the estimated average annual growth rate of the country's population for 1950 is approximately 1.156.
To estimate the average annual growth rate of the country's population for 1950 using the given model, we need to substitute the value of x as 1950-1900 = 50 into the equation.
y = -0.0000088(50)^3 + 0.00214(50)^2 - 0.202(50) + 7.906
Calculating the expression:
y = -0.0000088(125000) + 0.00214(2500) - 0.202(50) + 7.906
= -1.1 + 5.35 - 10.1 + 7.906
= 1.949
Therefore, the estimated average annual growth rate of the country's population for 1950 is approximately 1.949.