AIDS Cases From 1993 to 2003 the cumulative number N of AIDS cases in thousands

Question

AIDS Cases From 1993 to 2003 the cumulative number
N of AIDS cases in thousands can be approximated by, N= -2x squared +76X +430, where x=0 corresponds to the year 1993

year 1993 1995 1997 1999 2001 2003
cases 422 565 677 762 844 930


(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)?

Explanation / Answer

a) For 1993, putting x=0, N = -2*0^2+76*0+430 = 430 For 1995, putting x=2, N = -2*2^2+76*2+430 = 574 For 1997, putting x=4, N = -2*4^2+76*4+430 = 702 For 1999, putting x=6, N = -2*6^2+76*6+430 = 814 For 2001, putting x=8, N = -2*8^2+76*8+430 = 910 For 2003, putting x=10, N=-2*10^2+76*10+430 = 990 b) The equation approximates to a good degree initially, but for further dates from 1993, the approximation gradually becomes a little more off the actual number of cases. c) N = -2(x-43)(x+5) d) For 1993, putting x=0, N=-2(0-43)(0+5)= 430 For 1995, putting x=2, N=-2(2-43)(2+5) = 574 For 1997, putting x=4, N=-2(4-43)(4+5) = 702 For 1999, putting x=6, N=-2(6-43)(6+5) = 814 For 2001, putting x=8, N=-2(8-43)(8+5) = 910 For 2003, putting x=10, N=-2(10-43)(10+5) = 990 Answers agree with those found in part (a). Read more: Math Questions - AIDS Cases From 1993 to 2003 the cumulative number of N of - JustAnswer http://www.justanswer.com/math/4rk9k-aids-cases-1993-2003-cumulative-number.html#ixzz1I89AuHbO

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