Differential Equations

At what population value does the logistic model reach its carrying capacity?

If the series $\sum_{n=1}^{\infty} \frac{(-1)^n}{\sqrt{n}}$ converges, which test provides the justification?

Given that cell culture grows according logistical equation $\frac{dp}{dt}=rp\left(1-\frac{p}{C}\right)$, if researcher wishes double quantity cells within hours & knows exact doubling-time under current conditions, how she adjust paramet...

Which term in the logistic differential equation $\frac{dP}{dt} = kP \left(1 - \frac{P}{L} \right)$ shows slowing down population growth?

For a modified logistic model given by $\frac{dN}{dt}=rN\left(1-\left(\frac{N^n}{K^n}\right)\right)$ where $n>1$, determine which initial condition will lead to an inflection point occurring at exactly half of carrying capacity.

For what values of $x$ does the power series representation $\sum_{n=0}^{\infty} \frac{(x-3)^n}{5^n}$ converge?

Which of the following statements is true regarding the logistic model's behavior when the initial population is below the carrying capacity?

Which condition must be satisfied for a differential equation $\frac{dP}{dt}=kP(1-\frac{P}{L})$ where P represents population at any time t and L is carrying capacity?

For what value of M does adding a term -MNP change a standard logistic growth model into a predator-prey model that exhibits cyclical behavior around non-trivial steady states if P represents predator population?

Given a logistic model $\frac{dP}{dt} = kP \left(1 - \frac{P}{C} \right)$ where $k$ is a positive constant and $C$ is the carrying capacity, what value of $P$ makes $\frac{dP}{dt}$ equal to zero?