Question

A country's census lists the population of the country as 246 million in 1990, 268 million in 2000, and 286 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 population in 2020 and in 2030.

2020 million

2030 million

Answer 1

Given ,

Year	1990	2000	2010
Population (million)	246	268	286

But given that the year 2000 to be x = 0 ,

then , for the year 1990 , let x = -1

and for year 2010 , let x = 1

Thus we get -

xi	-1	0	1
yi	246	268	286

Now , let the general form of the quadratic equation be -

Using the values of x and y from the table in the above equation , we have -

i.e., we have -

i.e.,

Now , using equation (ii) in (i) and (iii) , we have -

simplifying above equations , we get -

Adding equations (iv) and (v) , we get -

Using a = 2 , in equation (v) , we have -

i.e.,

Hence from equation (1) , we have the required quadratic polynomial , i.e.,

Now , from year 2020 , x = 2 ,

Therefore ,

Thus , the population in year 2020 = 300 million .

Similarly , for year 2030 , x = 3 ,

Therefore ,

Thus , the population in year 2030 = 310 million .