Biology · Organisms and Populations · NEET
Because the population multiplies by a fixed factor in each time step instead of adding a fixed number. Adding the same amount each time is arithmetic (a straight line). Multiplying by the same factor each time is geometric, so the numbers grow faster and faster - 2, 4, 8, 16 and so on. NCERT uses the words exponential and geometric to mean the same growth pattern.
In the exponential model the growth rate (dN/dt = rN) itself depends on N. As N gets bigger, dN/dt gets bigger too, so the curve stays low and flat at first and then bends sharply upward. That flat-start, steep-rise shape looks like the letter J. There is no upper flattening because resources are assumed to be unlimited.
dN/dt is the change in population size per unit time (the growth rate). r is the intrinsic rate of natural increase, equal to (b - d), the per-capita birth rate minus the per-capita death rate. N is the current population size. So the equation says the population grows in proportion to how many individuals are already present - more individuals means faster growth.
Only when resources (food and space) are unlimited, which is an ideal condition. NCERT notes this is why exponential growth is not fully realistic - in nature resources become limiting, competition begins, and growth slows into the logistic (S-shaped) pattern. Exponential growth can still be seen for a short time, for example bacteria in fresh culture or a species colonising a new habitat.
If the per-capita birth rate equals the per-capita death rate, then r = (b - d) = 0, so dN/dt = rN = 0. The population size does not change at all - it stays flat. This is a favourite NEET numerical trick: even after many generations the number stays the same, so no J-curve forms.
Match List I with List II: List I: A. Logistic growth B. Exponential growth List II: I. Unlimited resource availability condition II. Limited resource availability condition (only the growth-model pairing is shown here)
Consider a population of 10 million cells with a per-capita birth rate of 0.002 (per unit time) and a per-capita death rate of 0.002 (per unit time). The expected number of cells after 10 generations is ______.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Yes. When you plot N against time for the exponential (geometric) model, the plot is the J-shaped curve. They describe the same unlimited-resource growth.
dN/dt = rN is the differential (rate) form showing how fast the population grows at any instant. Nt = N0 e^rt is the integral form that lets you calculate the actual population size after time t. Both describe exponential growth.
r is the intrinsic rate of natural increase, equal to per-capita birth rate minus per-capita death rate (b - d). A higher r means faster exponential growth.
Because no habitat has unlimited resources. As numbers rise, food and space become limiting and competition begins, so real growth slows into the logistic S-shaped curve. NCERT calls the logistic model the more realistic one.
