Population Growth: Exponential vs. Logistic Models

Biology Grades High School 7:32 Video
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Lesson Description

Explore the dynamics of population growth, comparing exponential and logistic models, and understanding the impact of carrying capacity.

Video Resource

Exponential and logistic growth in populations | High school biology | Khan Academy

Khan Academy

Duration: 7:32
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Key Concepts

  • Exponential Growth
  • Logistic Growth
  • Carrying Capacity
  • Population Dynamics
  • Limiting Factors

Learning Objectives

  • Define and differentiate between exponential and logistic population growth.
  • Explain the concept of carrying capacity and its role in limiting population size.
  • Apply mathematical models to predict population growth patterns.
  • Identify factors that limit population growth in real-world scenarios.

Educator Instructions

  • Introduction (5 mins)
    Begin by asking students about their understanding of population growth. Discuss examples of rapidly growing populations (e.g., bacteria, invasive species) and what factors might limit their growth. Briefly introduce the concepts of exponential and logistic growth as mathematical models to explain these phenomena.
  • Video Presentation (10 mins)
    Play the Khan Academy video 'Exponential and logistic growth in populations'. Instruct students to take notes on the key differences between exponential and logistic growth, and the role of carrying capacity.
  • Discussion and Analysis (15 mins)
    Facilitate a class discussion based on the video. Focus on the following: (a) How is exponential growth modeled mathematically? (b) What are the assumptions of exponential growth, and why are they often unrealistic? (c) How does logistic growth incorporate the concept of carrying capacity? (d) What are some real-world examples of populations exhibiting logistic growth? (e) How do limiting factors affect population size?
  • Mathematical Modeling Activity (15 mins)
    Present students with a hypothetical scenario involving a population of organisms (e.g., deer in a forest). Provide data on birth rates, death rates, and the carrying capacity of the environment. Guide students to use simple equations (provided) to model both exponential and logistic growth over a set period. Compare and contrast the outcomes of the two models.
  • Wrap-Up and Assessment (5 mins)
    Summarize the key concepts of the lesson. Administer a short multiple-choice or fill-in-the-blank quiz to assess student understanding (see quizzes below).

Interactive Exercises

  • Graphing Population Growth
    Provide students with data points representing population size over time. Have them plot the data on a graph and determine whether the growth pattern is closer to exponential or logistic. If logistic, have them estimate the carrying capacity.
  • Limiting Factors Brainstorm
    Divide students into small groups. Assign each group a different environment (e.g., a pond, a forest, a desert). Have them brainstorm a list of factors that could limit the population growth of various organisms in that environment.

Discussion Questions

  • What are some real-world examples of populations that initially exhibit exponential growth?
  • How does carrying capacity influence the shape of the logistic growth curve?
  • What are some factors that might cause the carrying capacity of an environment to change over time?
  • In what situations would an exponential growth model be a useful approximation of real-world population growth?
  • Can you think of examples where human activity has significantly altered the carrying capacity for other species?

Skills Developed

  • Mathematical Modeling
  • Data Analysis
  • Critical Thinking
  • Scientific Reasoning

Multiple Choice Questions

Question 1:

Which type of population growth model assumes unlimited resources?

Correct Answer: Exponential

Question 2:

What is the term for the maximum population size that an environment can sustain?

Correct Answer: Carrying Capacity

Question 3:

In a logistic growth model, what happens to the growth rate as the population approaches carrying capacity?

Correct Answer: It decreases

Question 4:

Which of the following is NOT a limiting factor on population growth?

Correct Answer: Unlimited Space

Question 5:

A population growing exponentially exhibits a _____ shaped curve when graphed.

Correct Answer: J

Question 6:

What is the main difference between exponential and logistic growth?

Correct Answer: Logistic growth considers carrying capacity.

Question 7:

If a population exceeds its carrying capacity, what is likely to happen?

Correct Answer: The population will continue to grow exponentially.

Question 8:

Which model of population growth is more realistic in natural environments?

Correct Answer: Logistic

Question 9:

What shape is the curve of logistic growth?

Correct Answer: L-shaped

Question 10:

In the exponential growth equation, the exponent represents:

Correct Answer: The growth rate

Fill in the Blank Questions

Question 1:

___________ growth occurs when a population increases at a constant rate per unit of time.

Correct Answer: Exponential

Question 2:

The ___________ is the maximum number of individuals that an environment can support.

Correct Answer: Carrying Capacity

Question 3:

___________ growth incorporates the concept of carrying capacity.

Correct Answer: Logistic

Question 4:

Factors that limit population size are known as ___________.

Correct Answer: Limiting Factors

Question 5:

Exponential growth is often represented by a _____ shaped curve.

Correct Answer: J

Question 6:

A more realistic model for population growth is ___________ growth.

Correct Answer: Logistic

Question 7:

When a population reaches carrying capacity, the growth rate tends to ___________.

Correct Answer: Decrease

Question 8:

Competition for resources, predation, and disease are all examples of ___________.

Correct Answer: Limiting Factors

Question 9:

The curve associated with logistic growth is _____-shaped.

Correct Answer: S

Question 10:

The rate of growth is constant with __________ growth.

Correct Answer: Exponential

Educational Standards

B.LS2.1:Use mathematical and/or computational representations to support explanations of factors that affect carrying capacities of ecosystems at different scales. B.LS2.2:Use mathematical representations to support and revise explanations based on evidence about factors affecting biodiversity and populations in ecosystems of different scales. B.LS4.2:Construct an explanation based on evidence that biological diversity is influenced by (1) the potential for a species to increase in number, (2) the heritable genetic variation of individuals in a species due to mutation and sexual reproduction, (3) competition for limited resources, and (4) the proliferation of those organisms that are better able to survive and reproduce in the environment.

Teaching Materials

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