Choose the one alternative that best completes the statement or answers the question.
-The logistic growth function $f ( t ) = \frac { 12,000 } { 1 + 199 e ^ { - 1.7 t } }$ models the number of people who have become ill with a particular infection t weeks after its initial outbreak in a particular community. How many people were ill after 9 weeks?
A) 12,000 people
B) 11,999 people
C) 12,200 people
D) 540 people

Question

Quizplus · Accepted Answer

To find the number of people ill after 9 weeks, substitute $t = 9$ into the logistic growth function and solve for $f(9)$:$$f(9) = \frac{12,000}{1 + 199e^{-1.7 \times 9}}$$$$f(9) = \frac{12,000}{1 + 199e^{-15.3}}$$$$f(9) \approx \frac{12,000}{1 + 199 \times 2.2 \times 10^{-7}}$$$$f(9) \approx \frac{12,000}{1 + 0.0438}$$$$f(9) \approx \frac{12,000}{1.0438}$$$$f(9) \approx 11,999$$Therefore, approximately 11,999 people were ill after 9 weeks.

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