# Calculus

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 Curve Expert or another curve modelling program, determine an equation that can be used to model this data.

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?

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