A countrys census lists the population of the country as 246

A country\'s census lists the population of the country as 246 million in 1990, 278 million in 2000, and 306 million in 2010. Fit a second-degree polynomial these three points. (Let the year 2000 be x = 0 and let p(x) represent the population in millions.) Use this polynomial to predict the population in 2020 and in 2030.

Solution

x =-10 , 246 million ; x = 0, 278 million ; x= 10 , 306 million

2nd degree polnomial : ax^2 +bx +c.Plug these three points and frame three equations.

246 = 100a -10b + 278

-32 = 100a -10b

278 = c

32 = 100a - 10b -----(1)

306 = 100a + 10b + 278

28 = 100a +10b -----(2)

Solve the above equations : a = 60/200 = 0.3 ; b= -0.2

p(x)= 0.3x^2 -0.2x + 278

in 2020 p( x= 20) = 394 million

in 2030 p( x= 30) = 542 million