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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.)

User Snewedon
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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

User Trama
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