Which is correctly labelled with respect to the given diagram?

The correct answer is Option (3) → A: Carrying capacity

The graph shows the two growth curves of a population. Curve B rises steeply without any limit; this J-shaped curve is exponential growth (dN/dt = rN). Curve C rises slowly, speeds up, slows down and levels off; this sigmoid curve is logistic growth. The dotted line A, where curve C levels off, is the carrying capacity (K): the largest number the habitat’s resources can support.

Option (1) B: Logistic growth curve — Incorrect. B is the J-shaped curve of exponential growth, with the equation dN/dt = rN written beside it. It is not logistic.

Option (2) C: Exponential growth curve — Incorrect. C is the sigmoid curve with the equation dN/dt = rN((K – N)/K). That is logistic growth, not exponential.

Option (3) A: Carrying capacity — Correct. A is the horizontal dotted line that the logistic curve approaches and does not cross. It marks the carrying capacity, K.

Option (4) C: Carrying capacity — Incorrect. C is a curve that changes with time; carrying capacity is the fixed level shown by line A.

Note: Figure 11.3 has turned up here wearing new letters, like an old friend in a new shirt. Learn each curve by its shape and equation, and a change of labels will not fool you.

NCERT Extract:
Growth Models – “… In nature, a given habitat has enough resources to support a maximum possible number, beyond which no further growth is possible. Let us call this limit as nature’s carrying capacity (K) for that species in that habitat. A population growing in a habitat with limited resources show initially a lag phase, followed by phases of acceleration and deceleration and finally an asymptote, when the population density reaches the carrying capacity. A plot of N in relation to time (t) results in a sigmoid curve.”

Figure 11.3 Population growth curve: a when responses are not limiting the growth, plot is exponential; b when responses are limiting the growth, plot is logistic; K is carrying capacity