This Question 1 pt 5 of 6 0 complete The 2000 census in a pa

This Question: 1 pt 5 of 6 (0 complete) The 2000 census in a particular area gives us an age distribution that is approximately given (in millions) by the function f(x)= 39 2 + 2.06x-0705x2 where x varies from 0 to 9 decades. The population of a given age group can be found by integrating this function over the interval for that ag a. Find the integral over the interval [o.S9] Round to the nearest integer as needed) What does this integral represent? O A. The number of people in this area increased by about 265 milion people aged 0 to 90 in 200 O B. The total number of people in this area under 9 years old was about 265 in 2000 O C. The total number of people in this area aged 0 to 90 was about 265 million in 2000 0 D. About 265 million people aged 0 to 90 have ever lived in this area from year 0 through 2000. b. Find the number of people alive in 2000 that were born in the sixties, that is, those in the range of 3 to 4 decades in 2000 million Round to the nearest integer as needed)

Solution

f(x) = 39.2 + 2.06x – 0.705x²

(a) ₀⁹(39.2 + 2.06x – 0.705x²)dx = 39.2x + 2.06*x^2/2 – 0.705x^3/3  

      = 39.2x + 1.03x^2 – 0.235*x^3

      = 39.2*9 + 1.03*9^2 – 0.235*9^3 = 264.915 ~265 million

265 million people who are between 0 to 90 years old

(b) 39.2x + 1.03x^2 – 0.235*x^3    [limit 3 to 4]

     = [39.2*4 + 1.03*4^2 – 0.235*4^3] – [39.2*3 + 1.03*3^2 – 0.235*3^3]

     = 158.24 - 120.525 = 37.715 ~ 37 million people