$\text { The logistic function } P ( t ) = \frac { 20 } { 1 + 0.5 e ^ { - 0.2 t } } \text { models the growth of a population. }$ Identify the value of k.
A)1.7
B)2.2
C)0.2
D)20
E)0.5

Question

Quizplus · Accepted Answer

The logistic function is given by:

$$
P(t) = \frac{20}{1 + 0.5e^{-0.2t}}
$$

We can rewrite this as:

$$
P(t) = \frac{20}{1 + \frac{1}{2}e^{-0.2t}}
$$

Comparing this to the standard form of the logistic function:

$$
P(t) = \frac{K}{1 + Ae^{-kt}}
$$

we can see that $K = 20$ and $A = \frac{1}{2}$. Therefore, we need to find the value of $k$.

By comparing the two forms, we can see that:

$$
k = 0.2
$$

Therefore, the answer is (C) 0.2.

The logistic function P(t)=201+0.5e−0.2t models the growth of a population. \text { The logistic function } P ( t ) = \frac { 20 } { 1 + 0.5 e ^ { - 0.2 t } } \text { models the growth of a population. } The logistic function P(t)=1+0.5e−0.2t20​ models the growth of a population.

$\text { The logistic function } P ( t ) = \frac { 20 } { 1 + 0.5 e ^ { - 0.2 t } } \text { models the growth of a population. }$