Problema Solution
AIDS Cases From 1993 to 2003 the cumulative number
N of AIDS cases in thousands can be approximated by
N = -2x^2 + 76x + 430, where x = 50 corresponds to the year 1993.
(a) Use the equation to find N for each year in the table.
(b) Discuss how well this equation approximates the data.
(c) Rewrite the equation with the right side completely
factored.
(d) Use your equation from part (c) to find N for each year
in the table. Do your answers agree with those found in
part (a)?
Table:
Year 1993 1995 1997 1999 2001 2003
Cases 422 565 677 762 844 930
Answer provided by our tutors
1993, x = 50
N = -2(50)2 + 76(50) + 430
= -770
1995, x = 52
N = -2(52)2 + 76(52) + 430
= -1026
1997, x = 54
N = -2(54)2 + 76(54) + 430
= -1298
1999, x = 56
N = -2(56)2 + 76(56) + 430
= -1586
2001, x = 58
N = -2(58)2 + 76(58) + 430
= -1890
2003, x = 60
N = -2(60)2 + 76(60) + 430
= -2210
N = -2x2 + 76x + 430
N =-2(x2 - 38x - 215)
N = -2(x - 43)(x + 5)