The Logistic Function is sometimes a more realistic growth model than the typical exponential growth models used. Most populations do not grow exponentially without bound. Once the population has grown to reach its environment’s maximum capacity, it will level off around the carrying capacity.
Notes
Practice Questions
\(\textbf{1)}\) The number of people infected with dance fever after t days at the beach is modeled by the following function, \(P(t)= \frac{2200}{1+99e^{-0.5t}}\), how many people were infected at time \(t=0\)?
The answer is \( 22 \) people.
\(\textbf{2)}\) The number of people infected with dance fever after t days at the beach is modeled by the following function, \(P(t)= \frac{2200}{1+99e^{-0.5t}}\), after 4 days, about how many people will be infected?
The answer is \( 153 \) people.
\(\textbf{3)}\) The number of people infected with dance fever after t days at the beach is modeled by the following function, \(P(t)= \frac{2200}{1+99e^{-0.5t}}\), what is the maximum people of people to be infected with dance fever?
The answer is \( 2200 \) people.
\(\textbf{4)}\) The number of people infected with dance fever after t days at the beach is modeled by the following function, \(P(t)= \frac{2200}{1+99e^{-0.5t}}\), at what time will 1000 people be infected with dance fever?
The answer is \( 8.8 \) days.
\(\textbf{5)}\) Find the following for the graph of \(f(x)= \frac{2200}{1+99e^{-0.5x}}\)?
There is no x-intercept
The y-intercept is \( 22 \)
The horizontal asymptotes are \(\,y=0\,\) and \(\,y=2200\)
There are no vertical asymptotes
\(\textbf{6)}\) Find the following for the graph of \(f(x)= \frac{10}{1+e^{-x}}\)?
There is no x-intercept
The y-intercept is \( 5 \)
The horizontal asymptotes are \(\,y=0\,\) and \(\,y=10\)
There are no vertical asymptotes
\(\textbf{7)}\) Find the following for the graph of \(f(x)= \frac{10}{1+4e^{-x}}\)?
There is no x-intercept
The y-intercept is \( 2 \)
The horizontal asymptotes are \(\,y=0\,\) and \(\,y=10\)
There are no vertical asymptotes
See Related Pages\(\)
