Question

(a) Draw a graph for a population whose population density has reached the carrying capacity.
(b) Out of the two population growth curves, which one is considered a more realistic for most populations? Why?
(c) Draw a growth curve where resources are not limiting for the growth of a population and give its equation.

Hint:

Logistic growth reflects real-world constraints like carrying capacity, while exponential growth occurs only under ideal, unlimited conditions, as described by $N_t = N_0 e^{rt}$.

Answer 1

Step 1: For (a), a population at carrying capacity (K) follows a logistic growth curve, where growth slows as the population reaches K, leveling off. The graph below shows population size (N) over time, rising steeply at first, then plateauing at K.
Step 2: For (b), the logistic growth curve is more realistic for most populations because it accounts for limiting factors like resources and space, leading to a carrying capacity (K), unlike exponential growth, which assumes unlimited resources and is unsustainable in nature.
Step 3: For (c), when resources are not limiting, the population follows an exponential growth curve, which rises continuously. The equation for exponential growth is $N_t = N_0 e^{rt}$, where $N_t$ is population size at time $t$, $N_0$ is initial population size, $r$ is the growth rate, and $e$ is the base of natural logarithms. The chart below represents this growth: