Graphing logistic functions Quiz 1

Question 1

For a general function, $$y=\dfrac{2}{1+3{{e}^{-4x}}}$$, calculate both the y-intercept and x-intercept

Accepted Answer

y-intercept$$= (0,\dfrac{1}{2})$$,x-intercept=none

Answer

y-intercept $$= (0,\dfrac{1}{2})$$, x-intercept =-12

Answer

y-intercept$$= (2,1)$$,x-intercept = 2

Answer

y-intercept = none x-intercept = none

Question 2

At a given office, the population of the number of employees is $$E(t)$$. A statistician calculated that the employee population $$E(t)$$ satisfied by the logistic differential equation $$\dfrac{dE}{dt}=16E	imes (16-\dfrac{E}{24000})$$such that the variable $$t$$ is used to measure the number of employees in the office in years. Calculate the carrying capacity of the office.

Accepted Answer

Carrying Capacity $$=384000$$

Answer

Carrying Capacity $$=1500$$

Answer

Carrying Capacity$$=256$$

Answer

Carrying Capacity $$=24000$$

Question 3

The following information is given, $$c=2400,(0,8),(6,6)$$. Solve for the logistic function in terms of x.

Accepted Answer

$$f(x)=\dfrac{2400}{1+299	imes {{\left( \sqrt[6]{\dfrac{399}{299}} ight)}^{x}}}$$

Answer

$$f(x)=\dfrac{2400}{1+399	imes {{\left( \sqrt[3]{\dfrac{399}{299}} ight)}^{x}}}$$

Answer

$$f(x)=\dfrac{2400}{1+299	imes {{\left( \sqrt[5]{\dfrac{399}{299}} ight)}^{x}}}$$

Answer

$$f(x)=\dfrac{2400}{1+299	imes {{\left( \sqrt[8]{\dfrac{399}{299}} ight)}^{x}}}$$

Question 4

For a logistic function that models forecast data monthly with the parameters: $$n=1,{{x}_{o}}=0,C=1$$, what is the simplified form of the logistic function?

Accepted Answer

$$\dfrac{1}{2}+\dfrac{1}{2}	anh (\dfrac{x}{2})$$

Answer

$$\dfrac{1}{1+{{e}^{-x}}}$$

Answer

$$\dfrac{1}{3}+\dfrac{1}{3}	an (\dfrac{x}{2})$$

Answer

$$\dfrac{{{e}^{-x}}}{{{e}^{-x}}+1}$$

Question 5

How many years will it take for a yeast population to reach $$99000$$ given that its growth function is modelled by $$f(t)=\dfrac{750000}{1+{{e}^{-0.36(t-60)}}}$$

Accepted Answer

$$t=54.77$$

Answer

$$t=14.4$$

Answer

$$t=38.9$$

Answer

$$t=71.4$$