A population satisfies $\frac{dP}{dt}=0.0001P\left(200-P\right)$. What are the carrying capacity and the constant $k$ in the form $kP\left(1-\frac{P}{L}\right)$?

A population is modeled by $P(t)=\frac{1200}{1+5e^{-0.02t}}$. What is the carrying capacity, and what was the initial population?

For $\frac{dP}{dt}=0.02P\left(1-\frac{P}{200}\right)$, with $P$ in cells and $t$ in hours, at what population is the population growing FASTEST, and how fast is it growing then?

A population is modeled by $P(t)=\frac{800}{1+9e^{-0.04t}}$. What is the carrying capacity, and what was the initial population?

A population satisfies $\frac{dP}{dt}=0.1P\left(1-\frac{P}{3000}\right)$ with $P(0)=750$. What is ${\lim }_{t\to \infty }P(t)$?

A fish population in a lake satisfies $\frac{dP}{dt}=0.25P\left(1-\frac{P}{1600}\right)$, where $P$ is in fish and $t$ in years. What is the carrying capacity?

A yeast culture satisfies $\frac{dP}{dt}=0.08P\left(1-\frac{P}{200}\right)$, where $P$ is in cells and $t$ in hours. What is the carrying capacity?

A population satisfies $\frac{dP}{dt}=0.1P\left(1-\frac{P}{2000}\right)$ with $P(0)=1000$. What is ${\lim }_{t\to \infty }P(t)$?

A population satisfies $\frac{dP}{dt}=0.08P\left(1-\frac{P}{1000}\right)$ with $P(0)=2000$. What is ${\lim }_{t\to \infty }P(t)$?

A population is modeled by $P(t)=\frac{1200}{1+9e^{-0.04t}}$. What is the carrying capacity, and what was the initial population?

A population satisfies $\frac{dP}{dt}=0.0001P\left(400-P\right)$. What are the carrying capacity and the constant $k$ in the form $kP\left(1-\frac{P}{L}\right)$?

A town's population satisfies $\frac{dP}{dt}=0.05P\left(1-\frac{P}{2000}\right)$, where $P$ is in people and $t$ in years. What is the carrying capacity?

A town's population satisfies $\frac{dP}{dt}=0.4P\left(1-\frac{P}{600}\right)$, where $P$ is in people and $t$ in years. What is the carrying capacity?

For $\frac{dP}{dt}=0.4P\left(1-\frac{P}{2400}\right)$, with $P$ in people and $t$ in years, at what population is the population growing FASTEST, and how fast is it growing then?

For $\frac{dP}{dt}=0.4P\left(1-\frac{P}{800}\right)$, with $P$ in cells and $t$ in hours, at what population is the population growing FASTEST, and how fast is it growing then?

A logistic solution starts at $P(0)=40$ with carrying capacity $800$. Which statement describes the graph of $P$ for $t>0$?

A deer herd on an island satisfies $\frac{dP}{dt}=0.4P\left(1-\frac{P}{1600}\right)$, where $P$ is in deer and $t$ in years. What is the carrying capacity?

For $\frac{dP}{dt}=0.04P\left(1-\frac{P}{1000}\right)$, with $P$ in students and $t$ in days, at what population is the population growing FASTEST, and how fast is it growing then?

A population satisfies $\frac{dP}{dt}=0.0005P\left(400-P\right)$. What are the carrying capacity and the constant $k$ in the form $kP\left(1-\frac{P}{L}\right)$?

A logistic solution starts at $P(0)=80$ with carrying capacity $400$. Which statement describes the graph of $P$ for $t>0$?