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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.)

Respuesta :

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:

[tex]P_1=P_0+rP_0(1-\frac{P_0}{c})[/tex]

Where:

[tex]\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}[/tex]

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

[tex]r=\frac{36}{100}=0.36[/tex]

Now, we plug in the values:

[tex]P_1=17+(0.36)(17)(1-\frac{17}{380})[/tex]

Solving the operations:

[tex]P_1=22.85[/tex]

Therefore, the population next year is 22.85

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