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

Suppose a population grows according to a logistic model with a carrying capacity of 7500 and 𝑘 = 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 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.