This Question: 1 pt 9 of 25 (7 complet e bar graph shows the numbers of births a

Question

This Question: 1 pt 9 of 25 (7 complet e bar graph shows the numbers of births and deaths in a country for six selected years. The functions and r of years after 2000. Answer parts a through c B(x)=74x2-14x + 4050 D(x)--36x2 + 19x + 2404 a. Write a function that models the change in the country's population for each year from 2000 through 2005 O A. (B-Dyo) 11.0x2-33x+ 1646 B. (BD)(x)=-2664x4 +191x3 + 2943 6x2 +43 294x+9,736.200 x + B 74x2- 14x +4050 D3.6x2+ 19x+ 2404 b. Use the function from part (a) to find the change in the country's population in 2003

Explanation / Answer

(a). The change in the country's population from the year 2000 onwards equals the difference between the births and the deaths, yearwise. Hence, the answer is B(x) - D(x) = (B-D)(x) = 7.4x2 - 14x +4050 -[ -3.6x2 + 19x + 2404] =  7.4x2 + 3.6x2 -(14x + 19x) +4050 - 2404 = 11x2 - 33x + 1646. The option A is the correct answer.

(b) In the year 2003, x = 3 ( 3years after the year 2000). Hence on substituting x = 3 in the change function (B-D)(x) =  11x2 - 33x + 1646 derived above, we have the change in the country's population in 2003 = 11*32 -33*3 + 1646 = 11*9 - 99 + 1646 = 99 -99 + 1646 = 1646 thousand i.e. 1646000.

(c) It is not possible to read the figures in the bar diagram, despite zooming as the image is very faint.

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