From 1993 to 2003 the cumulative number N of AIDS cases in thousands can be appr

Question

From 1993 to 2003 the cumulative number N of AIDS cases in thousands can be approximanted by N=2x2+76X+430, where x=0 corresponds to year 1993.

Year: 1993 1995 1997 1999 2001 2004
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 the answerw agree with those found in part (a)?

Explanation / Answer

a) N = 2x^2 + 76x + 430 I'll put it in the form (x, N): (0, 422) (2, 565) (4, 677) (6, 762) (8, 844) (10, 930) b) Pretty well - I drew the graph, and the points are close to it, as we'll see in (c) c) N = 2(x^2 + 38x + 215) d) Again, I'll list them in (x, N) form: (0, 430) - our original was 422 (2, 590) - our original was 565 (4, 766) - our original was 677 (6, 958) - our original was 762 (8, 1166) - our original was 844 (10, 1390) - our original was 930 (e) It looks like it gets less and less accurate as x increases.

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