   Chapter 52.4, Problem 1SB ### Biology: The Dynamic Science (Mind...

4th Edition
Peter J. Russell + 2 others
ISBN: 9781305389892

#### Solutions

Chapter
Section ### Biology: The Dynamic Science (Mind...

4th Edition
Peter J. Russell + 2 others
ISBN: 9781305389892
Textbook Problem

# How does the prediction of the exponential model of population growth differ from that of the logistic model?

Summary Introduction

To review:

The difference between the predictions of the logistic model and those of the exponential model of population growth.

Introduction:

The exponential model is applied when unlimited growth is experienced by populations, whereas the logistic model is applied when the population growth is limited. The population growth can be limited in a logistic approach because of the finite amount of available resources.

Explanation

In the exponential model, bacterial populations can be considered as ideal examples as they reproduce by binary fission, that is, the parent cell divides itself, producing two daughter cells. The population size of bacteria doubles, if no bacteria dies in each generation.

In contrast to bacteria, population size is increased with births and decreased by death rate. Over a time period:

Change in population size=Number of birthsNumber of deaths

The change in population size over time can be expressed in the mathematical form as follows:

ΔNΔt=BD

Where ∆N is the change in population size, ∆t is the change in time period, and B and D are the absolute numbers of birth rate and death rate, respectively.

There is a specified time period for per capita birth rates and death rates. For example, for fruit flies, the time is measured in days, whereas in humans, time is measured in years. So, the revised population growth equation is the change in population’s size during a given time period and it depends upon per capita birth rate, per capita death rate as well as the number of individuals in the population.

ΔNΔt=BD

=bNdN=(bd)N

Or, dNdt=(bd)N

This equation is the exponential model of the population, where dN/dt is the population growth rate, b and d are per capita birth and death rates, respectively. As “r” is also expressed as per individual per unit time, therefore it can be used in place of (b – d). The exponential growth equation can be written as follows:

dNdt=rN

The population growth becomes zero in a situation where birth rate becomes equal to death rate, r=0 and the population’s size does not change but the birth and death rate still occur

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