Q.What would be the per cent growth or birth rate per individual per hour for the same population mentioned in the previous question (Question 10)?

Intrinsic rate r = per-capita birth rate − per-capita death rate.

Exponential growth occurs when resources are unlimited, giving the simple growth equation dN/dt = rN.

When resources (food, space) in a habitat are unlimited, a population grows exponentially, described by dN/dt = rN, where N is population size, t is time, and r is the intrinsic rate of natural increase. This produces a J-shaped growth curve. In contrast, dN/dt = rN[(K-N)/K] describes logistic growth under limited/resource-constrained conditions (K = carrying capacity), giving an S-shaped curve - the other listed options are not the standard correctly-written growth equations.

The Verhulst-Pearl logistic growth equation models population growth that slows as it approaches the carrying capacity K.

Unlike exponential growth (dN/dt = rN), the logistic model accounts for limited resources: as population size N approaches the carrying capacity K, growth rate slows and eventually stops. The equation is dN/dt = rN[(K − N)/K], where the factor (K − N)/K approaches 1 when N is small (near-exponential growth) and approaches 0 as N approaches K (growth levels off), producing the characteristic sigmoid (S-shaped) growth curve.

The logistic (Verhulst-Pearl) growth model describes population growth that slows as it approaches the environment's carrying capacity K, captured by the equation dN/dt = rN(K-N)/K.

Unlike exponential growth (dN/dt = rN, or Nt = N0.e^rt), which assumes unlimited resources and grows indefinitely, the logistic model recognises that resources are always finite. It introduces the carrying capacity K — the maximum population size an environment can sustain — and the term (K-N)/K acts as a brake: when N is small relative to K, this term is close to 1 and growth is nearly exponential, but as N approaches K, the term approaches 0 and growth rate slows to zero, producing the characteristic S-shaped (sigmoid) growth curve seen in most natural populations with resource limits.

When resources (food, space) are not limiting, a population grows exponentially, producing a 'J'-shaped growth curve.

Population growth follows two idealised models: exponential growth, which occurs when resources in the environment are unlimited, allowing the population to grow at its maximum intrinsic rate (dN/dt = rN) without any environmental resistance — plotted, this produces a 'J'-shaped curve that keeps rising steeply. In contrast, when resources become limiting, growth slows as the population approaches the carrying capacity (K) of the environment, producing an 'S'-shaped (sigmoid) logistic growth curve instead.

Logistic growth includes the carrying-capacity term (K-N)/K.

The steep, rapidly rising middle segment of a sigmoid (S-shaped) growth curve is the logarithmic/exponential growth phase, before growth slows and levels off at carrying capacity.

When a population grows in a habitat with limited resources, it follows a sigmoid (verhulst-pearl logistic) growth curve with three broad phases: an initial lag phase (slow start), a steep logarithmic/exponential phase where numbers rise rapidly because resources are still abundant, and a final plateau where growth rate falls to near zero as the population approaches the carrying capacity (K) of the environment. The point marked X, on the steeply rising middle portion before the curve flattens toward "Equilibrium", corresponds to this logarithmic growth phase.