79.8k views
1 vote
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?

2 Answers

4 votes

Final answer:

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%.

User FutureJJ
by
7.8k points
5 votes

Answer:

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.

User Salisha
by
8.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.