Question 705002

SCQHARD

Suppose that the increase in a population can be modelled as $\frac{dN}{dt} = rN \frac{(K - N)}{K}$ where $N$ is the size of the population, $K$ is the carrying capacity, $r$ is the per capita growth rate and $t$ is time. Which of the following statements is correct?

(A)

When $N \approx 0$ , the population is nearly exponential.

(B)

When $N = K$ , the population goes extinct as $dN/dt$ goes to zero.

(C)

When $N \approx 0$ , the population growth $dN/dt$ is maximum.

(D)

When $N \approx K/4$ , the population growth $dN/dt$ is maximum.

Detailed Solution

When $N \approx 0$ , the term $(K-N)/K \approx 1$ . Thus, $\frac{dN}{dt} \approx rN$ , which is the equation for exponential growth.

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