Question

A country's census lists the population of the country as 254 million in 1990, 286 million in 2000, and 314 million in 2010. Fit a second-degree polynomial passing through these three points. (Let the year 2000 be x = 0 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

254 million in 1990, 286 million in 2000, and 314 million in 2010

Let the year 2000 be x = 0

so points are (-10,254),(0,286), (10,314)

put all points in above equation

system Ax=b is

augmented matrix is

solution is

so equation is

.

for the year 2020 take x=20

  millions in 2020

.

for the year 2030 take x=30

millions in 2030