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)=(c)/(1+ae^(-bt))`

where

c = carrying capacity

a = constant

b = growth rate

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

`f(0)=(c)/(1+a)=29`
`(80)/(1+a)=29`
`\therefore a=(51)/(29)`

now we have the function

`f(t)=(80)/(1+(51)/(29)e^(-bt))`

Now we just need to find b.

`f(t)=(80)/(1+(51)/(29)e^(-0.90t))`