A country's census

Question

A country's census lists the population of the country as 252 million in 1990, 286 million in 2000, and 312 million in 2010. Fit a second-degree polynomial passing through these three points. (Let the year 2000 be x = 0, the year 2020 be x = 20, and let p(x) represent the population in millions.)

p(x) = ________ million

Use this polynomial to predict the populations in 2020 and in 2030.

2020 ________ Million

2030 ________ Million

Answer 1

p(x) = Ax² + Bx + C = population, in millions, x years from the year 2000.

Since p(0) = 286, we get C = 286.

p(-10) = 100A - 10B + 286 = 252

p(10) = 100A + 10B + 286 = 312

100A - 10B = -34

100A +10B = 26

200A = -8

So, A = -1/25

100(-1/25) + 10B = 26

-4 + 10B = 26

10B = 30

B = 3

p(x) = (-1/25)x² + 3x + 286

Answer 2

p(x) = -0.04 X^2 + 3X + 286

p(20) = 330

p(30) = 340

You can either use a quadratic regression curve-fitting function on a calculator or set up and solve a three-by-three system of equations to do the same thing.

Since only 3 values were given, p(20) is exactly equal to the value given for x=20.