Question Type 5: Determining parameter values based on information on the logistic model Exercises

Given a logistic growth modelP(t)=rac{50}{1+Ce^{-0.6t}},and the initial population is $P(0)=10$, determine the value of $C$.

Write the logistic function for a population of bacteria with carrying capacity $L=8$, initial size $P(0)=2$, and growth constant $k=0.5$.

Given the logistic model$P(t)=\frac{20}{1+4e^{-0.3t}},$compute $P(5)$.

A species has carrying capacity $L=9$ and initial population $P(0)=10$ following a logistic model$P(t)=\frac{9}{1+Ce^{-kt}}.$Compute $C$.

Find the constant $C$ in the logistic functionP(t)=rac{100}{1+Ce^{-0.3t}},if the initial value is $P(0)=120$.

Formulate the logistic model$P(t)=\frac{L}{1+Ce^{-rt}}$given $L=10$, initial $P(0)=12$, and intrinsic growth rate $r=3$.

For a logistic model with $L=500$, $P(0)=50$, and $r=0.4$, find $P(4)$.

If a logistic population model is$P(t)=\frac{1000}{1+Ae^{-0.2t}},$and the population doubles from $P(0)=100$ to $P(5)=200$, find $A$.

Given $P(t)=\frac{1000}{1+9e^{-0.2t}}$, find the time $t$ at which $P(t)=800$.

A logistic curve with carrying capacity $1000$ has growth constant $0.1$ and initial population $100$. How long until the population reaches half the carrying capacity?

A logistic model has $L=200$, $P(0)=10$ and $P(5)=50$. Determine the growth constant $k$ in$P(t)=\frac{200}{1+Ce^{-kt}}.$

If a logistic population reaches $P(2)=80$ and $P(6)=160$ with carrying capacity $L=200$, and initial $P(0)=20$, find the growth rate $k$.

Fit a logistic model $P(t)=\frac{L}{1+Ce^{-kt}}$to data: $P(0)=5$ and $P(3)=20$, given carrying capacity $L=100$. Determine $C$ and $k$.