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.

• A. Zero population growth
• B. Declined growth
• C. Exponential growth
• D. None of the above

Answer 1

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 $\frac{dN}{dt}$ is equal to zero, therfore if we solve the equation $\frac{dN}{dt}=0.6\times N\left(\frac{1-N}{300}\right)$, we get N = 300.