Problem

Pathology—Botulism Cases: Botulism is a rare but serious illness caused by Clostridium bot...

Pathology—Botulism Cases: Botulism is a rare but serious illness caused by Clostridium botulinum bacteria. The bacteria may enter the body through wounds, or they may live in improperly canned or preserved food. (Source: National Center for Biotechnology Information.) The number of cases of botulism in the United States from 1980 to 2011 can be modeled by the quadratic function

f(x) = −0.11x2 − 0.48x + 87.77 0 ≤ x ≤ 31

where x represents the number of years since 1980, and f(x) represents the number of cases of botulism detected annually. (Source: Centers for Disease Control and Prevention.)

(a) According to the model, how many botulism cases were there in 2000?


(b) Recent regulations, including increased inspections of canned goods and banning Botox injections for minors, have resulted in a steady decrease in the number of cases of the deadly disease. Determine msec when x = 20 and Δx = 5, and interpret the result.

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