Quiz 7

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Show all work in a neat and organized fashion. Clearly indicate your answers.

10 points possible.

Use correct units!!

1. (5 pts.) The number of polio cases in 1949 can be modeled by the equation

C(x)= 42183.9 1+21484.3e-1.2489x

where C(x) is the number of cases, and x=1 at the end of January 1949, x=2 at the end of February 1949, etc. (based on data from Twelfth Annual Report, The National Foundation for Infantile Paralysis, 1949).

Use three increasingly close points to numerically estimate the instantaneous rate of change at the end of September 1949, i.e., C¢(9). For the three points, use x=9.1, x=9.01, and x=9.001. Do not round any answers. After the last calculation, give the correct units for C¢(9).

2. (5 pts.) (Based on data from HIV/AIDS Surveillance 1992 Year End Edition. ) The number of AIDS cases diagnosed between 1988 and 1991 is modeled by

f(x) = -1049.5x2+5988.7 x +33770.7

where f(x) is the number of AIDS cases and x is the number of years since 1988.

In this problem, you will find the rate of change in number of AIDS cases in 1990 by using the ``+h'' method.

Do not round your answers. Include correct units in part (d).

(a) Find the number of AIDS cases when x=2.

(b) Write a formula for the number of AIDS cases when x=2+h. Simplify your answer.

(c) Write a formula for the slope of the secant line connecting the points at x=2 and x=2+h. Simplify your answer.

(d) What is the limiting value of the slope formula in part (c) as h approaches 0?