A conservation organization releases coyotes into a preserve. After years, 40 4 There are70 coyotes in the preserve. The preserve has a carrying capacity of 175. Write a logistic Function that models the population of coyotes in the preserve.
A)
$$y = \frac { 175 } { 1 + 3.375 e ^ { - 0.202733 t } }$$
B)
$$y = \frac { 175 } { 1 + 3.375 e ^ { - 0.702733 t } }$$
C)
$$y = \frac { 175 } { 1 + 3.375 e ^ { - 0.402733 t } }$$
D)
$$y = \frac { 175 } { 1 + 4.875 e ^ { - 0.352733 t } }$$
E)
$$y = \frac { 175 } { 1 + 3.375 e ^ { - 1.002733 t } }$$

Question

A conservation organization releases coyotes into a preserve. After years, 40 4 There are70 coyotes in the preserve. The preserve has a carrying capacity of 175. Write a logistic Function that models the population of coyotes in the preserve. 
A)
$$y = \frac { 175 } { 1 + 3.375 e ^ { - 0.202733 t } }$$
B)
$$y = \frac { 175 } { 1 + 3.375 e ^ { - 0.702733 t } }$$
C)
$$y = \frac { 175 } { 1 + 3.375 e ^ { - 0.402733 t } }$$
D)
$$y = \frac { 175 } { 1 + 4.875 e ^ { - 0.352733 t } }$$
E)
$$y = \frac { 175 } { 1 + 3.375 e ^ { - 1.002733 t } }$$

Quizplus · Accepted Answer

The logistic function is given by $$y = \frac{L}{1 + Ae^{-kt}}$$, where $L$ is the carrying capacity, $A$ is a constant determined by the initial conditions, and $k$ is the growth rate. Given the carrying capacity $L = 175$ and the initial population of 40 growing to 70, we can solve for $A$ and $k$. The correct option, A, matches the structure of a logistic function with the given parameters, where $A = 3.375$ and $k = 0.202733$, fitting the expected form of the logistic growth model for the coyote population.

A Conservation Organization Releases Coyotes into a Preserve y=1751+3.375e−0.202733ty = \frac { 175 } { 1 + 3.375 e ^ { - 0.202733 t } }y=1+3.375e−0.202733t175​

A Conservation Organization Releases Coyotes into a Preserve $y = \frac { 175 } { 1 + 3.375 e ^ { - 0.202733 t } }$