### Video Transcript

Suppose a population grows
according to a logistic model with a carrying capacity of 7500 and ๐ equals
0.006. Write the logistic differential
equation for this information.

Weโre told which type of population
growth model to use in this question. So we can quote the standard
logistic differential equation. Itโs d๐ by d๐ก equals ๐๐
multiplied by one minus ๐ over ๐ฟ, where ๐ is the growth rate of the population
and ๐ฟ is the carrying capacity. Weโve 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 d๐ by d๐ก is
equal to 0.006 โ thatโs ๐๐ โ multiplied by one minus ๐ over 7500 โ thatโs ๐ฟ. Weโre only asked to write the
logistic differential equation. So thereโs no need for us to
attempt to solve this and weโre done.