Question

Suppose 29 blackberry plants started growing in a yard. Absent constraint, the blackberry plants will spread by 90% a month. If the yard can only sustain 80 plants, use a logistic growth model to estimate the number of plants after 4 months. plants

Answer 1

Logistic growth is modelled by the function

$f(t)=\frac{c}{1+ae^{-bt}}$

where

c = carrying capacity

a = constant

b = growth rate

we know that f(0) = 29; therefore,

$f(0)=\frac{c}{1+a}=29$$\frac{80}{1+a}=29$$\therefore a=\frac{51}{29}$

now we have the function

$f(t)=\frac{80}{1+\frac{51}{29}e^{-bt}}$

Now we just need to find b.

$f(t)=\frac{80}{1+\frac{51}{29}e^{-0.90t}}$