# Question Video: Writing the Differential Equation Describing a Population Growing According to a Logistic Model given the Carrying Capacity and the Growth Rate Mathematics • Higher Education

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

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### 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.

Weโre told which type of population growth model to use in this question. So we can quote the standard logistic differential equation. Itโs d๐ by d๐ก equals ๐๐ multiplied by one minus ๐ over ๐ฟ, where ๐ is the growth rate of the population and ๐ฟ is the carrying capacity. Weโ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 d๐ by d๐ก is equal to 0.006 โ thatโs ๐๐ โ multiplied by one minus ๐ over 7500 โ thatโs ๐ฟ. Weโre only asked to write the logistic differential equation. So thereโs no need for us to attempt to solve this and weโre done.