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 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‘ƒ by d๐‘ก equals ๐‘˜๐‘ƒ multiplied by one minus ๐‘ƒ 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‘ƒ by d๐‘ก is equal to 0.006 โ€” thatโ€™s ๐‘˜๐‘ƒ โ€” multiplied by one minus ๐‘ƒ 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.

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