Question

What do ‘a’ and ‘b’ represent in the following population growth curve?

• A. ‘a’ represents exponential growth when responses are not limiting the growth; and ‘b’ represents logistic growth when responses are limiting the growth.
• B. ‘a’ represents logistic grwoth when responses are not limiting the growth; ‘b’ represnrs exponential growth when responses are limiting the growth.
• C. ‘a’ represents carrying capacity and ‘b’ shows logistic growth when responses are limiting the growth.
• D. ‘a’ represents exponential growth when responses are not limiting the growth and ‘b’ shows carrying capacity

Answer 1

The Correct Option is A

Curve 'a' represents exponential growth. This occurs when resources are unlimited, and the population grows at its intrinsic rate of increase ($r$). The equation for exponential growth is:
\[ \frac{dN}{dt} = rN \]
where:
N is the population size
t is time 
r is the per capita rate of increase
Curve 'b' represents logistic growth. This occurs when resources become limited, and the population growth slows down as it approaches the carrying capacity ($K$) of the environment. The equation for logistic growth is:
\[ \frac{dN}{dt} = rN \left( \frac{K - N}{K} \right) \]
where $K$ represents the carrying capacity.