Q1CC Explain why a constant per capit... [FREE SOLUTION]

Chapter 53: Q1CC (page 1188)

Explain why a constant per capita rate of growth (r) for a population produces a curve that is J-shaped.

Short Answer

Expert verified

The population size (N) is not constant. It is either decreasing or increasing. The development of the population shows acceleration and produces a J-shaped curve when the per capita rate of growth is applied to a population that is growing exponentially.

Step by step solution

Change in population size

The number of resources available for members of the population determines the increase and decrease in the population size. For example, a population living in an unlimited and ideal environment shows an increase in population size.

They have all access to energy and ability to grow and reproduce. A population living with limited resources does not show rapid growth.

Exponential growth

Exponential growth is the pattern of growth that shows a constant increase in the size of the population at each instant time. This type of growth pattern is seen in a population that lives in an unlimited and ideal environment. The equation that represents exponential growth is \(\frac{{dN}}{{dt}} = rN\)

Exponential growth curve

In the equation \(\frac{{dN}}{{dt}} = rN\), the rate of increase of population size is denoted by \(\frac{{dN}}{{dt}}\) and \(rN\) represents current population size (N) multiplied with constant (r). The population, which shows exponential growth, increases at a constant rate per member.

Therefore, when population size is compared with time, it shows a J-shaped growth curve even though the per capita rate of population growth is constant. Over time, more individuals are added to the population, which results in progressively steeper curves.