Solve the problem.
-$$f ( t ) = \frac { 20,000 } { 1 + 399 \mathrm { e } ^ { - 1.4 t } }$$ particular infection t weeks after its initial outbreak in a particular community. How many people were ill after 5 weeks?
A)20,400 people
B)14,664 people
C)250 people
D)20,000 people

Question

Quizplus · Accepted Answer

To find the number of people ill after 5 weeks, substitute $t = 5$ into the given function: $$f(5) = \frac{20,000}{1 + 399e^{-1.4(5)}}$$ Simplifying inside the exponent first: $$-1.4 \times 5 = -7$$ Then, calculate the exponent: $$e^{-7}$$ is a very small number. Plugging this into the equation and solving gives a value close to 14,664, which matches option B.

Solve the Problem f(t)=20,0001+399e−1.4tf ( t ) = \frac { 20,000 } { 1 + 399 \mathrm { e } ^ { - 1.4 t } }f(t)=1+399e−1.4t20,000​

Solve the Problem $f ( t ) = \frac { 20,000 } { 1 + 399 \mathrm { e } ^ { - 1.4 t } }$