The table to right gives the prolpections of the population

The table to right gives the prolpections of the population of a country from 2000 to 2100. Answer parts (a) throught (c). Find a linear that models this data, with x equal to the number of yours after 2000 and f(x) equal to the population in millions f(\'x) =

Solution

Let the required linear function be f(x) = ax + b .

Now, when x = 10, f (x) = 309.5 so that 10a + b = 309.5...(1)

Also, when x = 20, f (20) = 330.2, so that 20a + b = 330.2...(2)

On subtracting equation 1 from equation 2, we get 20a + b - ( 10a + b ) = 330.2 - 309.5 or, 10a = 20.7 so that x = 2.07. Now, on substituting this value of a in the 1st equation, we get 20.7 + b = 309.5 , or, b = 309.5 - 20.7 or, b = 288.8. Thus, the required linear function is f ( x ) = 2.07x + 288.8

We can verify the result by (say) substituting x = 20 in this equation. Then the projected population in 2020 ought to be (2.07)20 + 288.8 = 41.4 + 288.8 = 330.2 which tallies with the figure provided.