Question

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= -0.0000084x^3 + 0.00211x^2 - 0.205x + 8.423

The estimated average annual growth rate of the country's population for 1950 is?

Answer 1

The estimated average annual growth rate for the country's population in 1950 is found by substituting x = 50 into the given polynomial equation, resulting in an estimated growth rate of 2.398%.

Step-by-step explanation:

The estimated average annual growth rate of the country's population for 1950 can be estimated by first substituting x = 50 into the given model equation.

Y = -0.0000084x^3 + 0.00211x^2 - 0.205x + 8.423

Now we plug in the value for 1950:

Y = -0.0000084(50)^3 + 0.00211(50)^2 - 0.205(50) + 8.423

After computation, the estimated annual growth rate is found:

Y = -0.0000084(125000) + 0.00211(2500) - 0.205(50) + 8.423

This equates to:

Y = -1.05 + 5.275 - 10.25 + 8.423

Finally,

Y = 2.398

The estimated annual growth rate for 1950 is 2.398%.

Answer 2

The average annual growth rate of a certain country's population for 1950, 1988, and 2010 are 2.398, 0.9985 and 0.2236 respectively.

Step-by-step explanation:

The given equation is

`Y=-0.0000084x^3+0.00211x^2-0.205x+8.423`

Where Y is the annual growth rate of a certain country's population and x is the number of years after 1900.

Difference between 1950 and 1900 is 50.

Put x=50 in the given equation.

`Y=-0.0000084(50)^3+0.00211(50)^2-0.205(50)+8.423`

`Y=2.398`

Therefore the estimated average annual growth rate of the country's population for 1950 is 2.398.

Difference between 1988 and 1900 is 88.

Put x=88 in the given equation.

`Y=-0.0000084(88)^3+0.00211(88)^2-0.205(88)+8.423`

`Y=0.9984752\approx 0.9985`

Therefore the estimated average annual growth rate of the country's population for 1988 is 0.9985.

Difference between 2010 and 1900 is 110.

Put x=110 in the given equation.

`Y=-0.0000084(110)^3+0.00211(110)^2-0.205(110)+8.423`

`Y=0.2236`

Therefore the estimated average annual growth rate of the country's population for 2010 is 0.2236.