Question

7. The following table displays the number of HIV diagnoses per year in a particular country. Year 1997 1998 1999 2000 2001 2002 2003 2004 2005 Diagnoses 2512 2343 2230 2113 2178 2495 2496 2538 2518 a. Using Geogebra or another curve modelling program, determine a polynomial equation that can be used to model this data. Include a picture showing the curve. b. Using this model, estimate the number of diagnoses in 1996 and in 2006. c. At what rate would the number of diagnoses be changing in 2006? d. Halfway through 2006, the number of new HIV diagnoses was found to be 1232. Assuming this rate stays fairly constant for the remainder of the year, does this new information change the modelling equation? If so, how would this change your answer to part (c)? If you were an advocate for furthering HIV and AIDS research and treatment programs, would you be encouraged or discouraged by these results?

Answer 1

. FIGURE::1

solutim. → Given, 1997 1998 1999 2005 2001 2002 2003 2004 2005 year Diagnosts) 2512 2342 9230 2113 2178 2495 296 2538 2518 (a) Here, The polynomial equation the fitted regression line į giun below y= -48.412 + 25.383 # 2 + From the scatter plot > • Я 25.383 % 48412 the Figure : 1 which is for the data given Figure fit with the and linear line or > straight line (6) Here, The number of diegnostics in 2006 2506 225 2 1996 () will Here, change the number rate 25.38 3 of diagnostics (d) Here, out If the 2006 iş 1232 f 16 model then becauye not cohich will change number of diagnosis in we include this in our model will be fitting value, also consider the estimate of coefferrent.

. FIGURE:: 2

plot 3000 2500 . . 2000 1500 1000 500 0 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006

plot 3000 2500 2000 y = 25.383x-48412 1500 1000 500 O 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006