📚 Topic Summary
Unrestricted population growth, at its core, describes how a population increases without any limitations such as food, space, or predators. This idealized model uses differential equations to express the rate of change in population size over time. The basic equation states that the growth rate is proportional to the current population size. This means the larger the population, the faster it grows. Understanding this model is crucial for making predictions in various fields like biology, economics, and even social sciences.
🧮 Part A: Vocabulary
Match the term with its definition:
- Term: Population Size
- Term: Growth Rate
- Term: Differential Equation
- Term: Proportionality Constant
- Term: Unrestricted Growth
- Definition: A constant representing the rate of population increase per individual.
- Definition: A mathematical equation that relates a function with its derivatives.
- Definition: Population increase without limitations.
- Definition: The number of individuals in a population at a specific time.
- Definition: The change in population size over a specific period.
(Match 1 with ?, 2 with ?, 3 with ?, 4 with ?, 5 with ?)
✍️ Part B: Fill in the Blanks
Unrestricted population growth is modeled by a __________ equation, where the rate of change of the __________ is proportional to the current __________. The proportionality constant, often denoted as $k$, represents the __________ per individual. This model assumes no __________ factors limiting growth.
🤔 Part C: Critical Thinking
Imagine you are modeling the growth of a bacterial colony in a petri dish. What real-world factors might eventually cause the growth to deviate from the predictions of the unrestricted growth model? Explain your reasoning.
