Question

Afield currently contains 17 mint plants. Absent constraints, the number of plants would increase by 36 %each year, but the field can only support a maximum of 380 plants. Use the logistic model to predict the plantpopulation the next year.The mint plant population next year will be:(Round to at least two decimal places.)

Answer 1

We are asked to use the logistic model to determine the population of plants given the constraints. The logistic growth model follows the next formula:

`P_1=P_0+rP_0(1-(P_0)/(c))`

Where:

`\begin{gathered} P_1=\text{ population the next year} \\ P_0=\text{ current population} \\ r=\text{ rate of growth absent constraints} \\ c=\text{ }capacity \end{gathered}`

Now, we are given that the growth rate is 36%, this in decimal form is:

`r=(36)/(100)=0.36`

Now, we plug in the values:

`P_1=17+(0.36)(17)(1-(17)/(380))`

Solving the operations:

`P_1=22.85`

Therefore, the population next year is 22.85