Question

17. Suppose 17 blackberry plants started growing in a yard. Absent constraint, the blackberry plants will spread by 90% a month. If the yard can only sustain 120 plants, use a logistic growth model to estimate the number of plants after 5 months. plants

Answer 1

Step 1: Write out the formula for logistic growth model

`P(t)=(KP_0e^(rt))/(K+P_0(e^(rt)-1))`
`\begin{gathered} \text{ Where} \\ K=\text{ the carrying capacity} \\ r=\text{ the growth rate (in decimal form)} \\ P_0=\text{ the initial population} \\ P(t)=\text{ the population at time t} \end{gathered}`

Step 2: Write out the given values and substitute them into the formula

`\begin{gathered} \text{ In this case,} \\ K=120 \\ r=(90)/(100)=0.9 \\ P_0=17 \\ t=5 \end{gathered}`

Hence,

`P(5)=(120*17* e^((0.9*5)))/(120+17(e^((0.9*5))-1))`

`P(5)=112`

Hence, the number of plants after 5 months is approximately 112