Solve the problem.
-The logistic growth function $\mathrm { f } ( \mathrm { t } ) = \frac { 57,000 } { 1 + 813.3 \mathrm { e } ^ { - 1.6 \mathrm { t } } }$ 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 became ill with this infection when the epidemic began?
A) 70 people
B) 57,000 people
C) 813 people
D) 814 people

Question

Quizplus · Accepted Answer

To find the number of people who became ill when the epidemic began, we set $t = 0$ in the logistic growth function and solve for $f(0)$: $$f(0) = \frac{57,000}{1 + 813.3e^{-1.6(0)}} = \frac{57,000}{1 + 813.3} = \frac{57,000}{814.3}$$ Since the choices are whole numbers and the calculation is meant to give an approximation, the closest number to the result of this calculation is 70 people.

Solve the Problem f(t)=57,0001+813.3e−1.6t\mathrm { f } ( \mathrm { t } ) = \frac { 57,000 } { 1 + 813.3 \mathrm { e } ^ { - 1.6 \mathrm { t } } }f(t)=1+813.3e−1.6t57,000​

Solve the Problem $\mathrm { f } ( \mathrm { t } ) = \frac { 57,000 } { 1 + 813.3 \mathrm { e } ^ { - 1.6 \mathrm { t } } }$