Solve the problem.
-The logistic growth function $\mathrm { f } ( \mathrm { t } ) = \frac { 16,000 } { 1 + 399.0 \mathrm { e } ^ { - 1.2 t } }$ 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) 40 people
B) 16,000 people
C) 399 people
D) 400 people

Question

Quizplus · Accepted Answer

To find the number of people who became ill when the epidemic began, set $t = 0$ in the logistic growth function and solve for $f(0)$: $f(0) = \frac{16,000}{1 + 399.0e^{-1.2(0)}} = \frac{16,000}{1 + 399} = \frac{16,000}{400} = 40$.

Solve the Problem f(t)=16,0001+399.0e−1.2t\mathrm { f } ( \mathrm { t } ) = \frac { 16,000 } { 1 + 399.0 \mathrm { e } ^ { - 1.2 t } }f(t)=1+399.0e−1.2t16,000​

Solve the Problem $\mathrm { f } ( \mathrm { t } ) = \frac { 16,000 } { 1 + 399.0 \mathrm { e } ^ { - 1.2 t } }$