If the initial size of a population was N-o- 10 and the population is growing at the rate of 0-6-Declined growth-Exponential growth-None of the above-

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Logistic Growth Graph

If the initia...

Question

If the initial size of a population was $N_{o} = 10$ and the population is growing at the rate of 0.6%, when will the population stabilize? The carrying capacity of the population is 300.

Zero population growth

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Declined growth

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Exponential growth

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None of the above

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Solution

The correct option is C
Exponential growth

The carrying capacity of a population is the maximum sustainable population density, therefore a population stops growing once it reaches its carrying capacity. The carrying capacity here is 300, therefore the population stops growing and stabilizes when it reaches 300. When the population stabilizes $\frac{d N}{d t}$ is equal to zero, therfore if we solve the equation $\frac{d N}{d t} = 0.6 \times N (\frac{1 - N}{300})$ , we get N = 300.

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If the initial size of a population was No=10 and the population is growing at the rate of 0.6%, when will the population stabilize? The carrying capacity of the population is 300.

If the initial size of a population was $N_{o} = 10$ and the population is growing at the rate of 0.6%, when will the population stabilize? The carrying capacity of the population is 300.