Suppose a population grows
according to a logistic model with a carrying capacity of 7500 and 𝑘 equals
0.006. Write the logistic differential
equation for this information.
We’re told which type of population
growth model to use in this question. So we can quote the standard
logistic differential equation. It’s d𝑃 by d𝑡 equals 𝑘𝑃
multiplied by one minus 𝑃 over 𝐿, where 𝑘 is the growth rate of the population
and 𝐿 is the carrying capacity. We’ve been given both of these
values in the question. So we just need to substitute them
into the logistic differential equation.
We have then that d𝑃 by d𝑡 is
equal to 0.006 — that’s 𝑘𝑃 — multiplied by one minus 𝑃 over 7500 — that’s 𝐿. We’re only asked to write the
logistic differential equation. So there’s no need for us to
attempt to solve this and we’re done.