3.5 Population Growth and Resource Availability

• Match the growth pattern with its characteristics:

  Exponential growth ↔️ Rapid and continuous increase

  Logistic growth ↔️ Slows as it nears carrying capacity
• What happens to population growth as resources become limited?

  It follows logistic growth
• A logistic growth pattern stabilizes at the carrying capacity
• An exponential growth pattern occurs when resources are abundant.
• What is the formula for exponential growth?

  \frac{dN}{dt} = r_{\text{\max}}N</latex>
• Logistic growth occurs when a population approaches its carrying capacity
• What is the formula for logistic growth?

  $\frac{dN}{dt} =$ r_{\text{\max}}N \left(1 - \frac{N}{K}\right)
• Match the population growth model with its characteristics:

  Exponential ↔️ Rapid and continuous increase

  Logistic ↔️ Slows as it nears carrying capacity

  Irruptive ↔️ Sudden growth followed by crash
• What characterizes irruptive growth?

  Sudden growth and decline
• Arrange the stages of logistic growth from start to finish:

  1️⃣ Rapid growth phase

  2️⃣ Growth slows as resources diminish

  3️⃣ Population approaches carrying capacity
• What is the formula for birth rate?

  $\frac{\text{Number of Births}}{\text{Population Size}}$
• Emigration refers to the movement of individuals out of a population.
• Understanding population dynamics is crucial for determining the carrying capacity
• What does the term 'emigration' refer to in population dynamics?

  Movement out of population
• Resource availability refers to the abundance of essential resources like food, water, and shelter
• Environmental conditions include factors like climate, temperature, and natural disasters.
• What happens to population growth when birth and immigration rates are high and death and emigration rates are low?

  Populations grow rapidly
• What does population growth refer to?

  Increase in population size
• Exponential growth occurs when a population expands at a constant rate with abundant resources
• The formula for exponential growth is $\frac{dN}{dt} =$ r_{\text{\max}}N.
• What does r_{\text{\max}} represent in the exponential growth formula?


  Maximum per capita increase
• Logistic growth occurs when population growth slows as it approaches the carrying capacity
• The formula for logistic growth includes the carrying capacity (K).
• What does $K$ represent in the logistic growth formula?


  Carrying capacity
• Exponential growth requires unlimited resources and no limiting factors
• Logistic growth reflects limited resource availability and competition.
• Match the growth type with its resource availability and formula:

  Exponential ↔️ Abundant resources, $\frac{dN}{dt} =$ r_{\text{\max}}N

  Logistic ↔️ Limited resources, $\frac{dN}{dt} =$ r_{\text{\max}}N \left(1 - \frac{N}{K}\right)
• What characterizes irruptive growth in a population?

  Sudden growth and crash
• Irruptive growth often occurs when environmental conditions suddenly change
• Irruptive growth follows a consistent pattern and stabilizes over time.

  False
• Match the growth model with its characteristics and mathematical representation:

  Exponential ↔️ Unlimited resources, $\frac{dN}{dt} =$ r_{\text{\max}}N

  Logistic ↔️ Limited resources, $\frac{dN}{dt} =$ r_{\text{\max}}N \left(1 - \frac{N}{K}\right)

  Irruptive ↔️ Fluctuating resources, Varies
• What is the maximum population size an environment can sustain called?

  Carrying capacity
• Exponential growth results in a rapid and continuous increase in population size.
• Logistic growth slows as the population approaches its carrying capacity
• Exponential growth occurs when resources are unlimited
• Exponential growth results in a rapid and continuous increase in population size.
• What does r_{\text{\max}} represent in the exponential growth formula?


  Maximum per capita rate
• Logistic growth occurs when resources become limited
• The growth rate in logistic growth slows as the population nears its carrying capacity.
• What is the carrying capacity represented by in the logistic growth formula?

  $K$