Q.Comment on the growth curve given below.

The graph shows a J-shaped growth curve, which is characteristic of exponential population growth under ideal conditions. When resources are unlimited and environmental resistance is absent, a population grows at its maximum intrinsic rate (r).

In the initial lag phase, growth is slow as the population establishes itself. This is followed by the exponential or log phase, where the curve rises steeply because the population size doubles at regular intervals—this constant interval is called the doubling time. The larger the population becomes, the faster it adds new individuals, creating the characteristic J-shape.

Such growth is typically seen in nature when:

• A species colonizes a new habitat with abundant resources
• Conditions are optimal with no predators or competitors
• The carrying capacity has not yet been reached …

A population's growth curve can only take one of two basic shapes: a J-shaped exponential curve (unlimited resources) or an S-shaped logistic curve (limited resources, bounded by a carrying capacity). The two are told apart by a single feature -- does the curve ever flatten out?

The growth curve described here never levels off: it starts slowly, then rises at an ever-increasing rate, with no sign of an upper plateau. This is exactly the behaviour predicted by the exponential growth equation:

Because the rate of increase ($dN/dt$) is directly proportional to the current population size ($N$), a larger population always adds individuals faster than a smaller one did -- there is no term in this equation that slows growth down as $N$ grows, unlike the logistic equation $dN/dt = rN(K-N)/K$, where the factor $(K-N)/K$ shrinks toward zero as $N$ approaches the carrying capacity $K$.

Integrating the exponential equation gives population size at any time:

Check the trend of the slope across the whole curve, not just its overall shape: a slope that keeps steepening everywhere, with no flattening anywhere, rules out logistic …