Population growth

Definition

Population growth describes the change in the number of individuals in a population over time. It can be modeled using exponential and logarithmic functions to predict future changes.

5 Must Know Facts For Your Next Test

1. Exponential growth of a population occurs when the growth rate is proportional to the current population size, leading to a rapid increase.
2. The formula for exponential growth is often written as $P(t) = P_0 e^{rt}$, where $P(t)$ is the population at time $t$, $P_0$ is the initial population, $r$ is the growth rate, and $e$ is Euler's number.
3. Logistic growth models are used when there are limiting factors that slow down population growth as it approaches a maximum sustainable size (carrying capacity).
4. The integral of an exponential function can be used to calculate total population over a period of time.
5. Doubling time in exponential growth can be calculated using the rule of 70: Doubling Time = 70 / Growth Rate.

Review Questions

• What is the formula for modeling exponential population growth?
• How does logistic growth differ from exponential growth?
• What mathematical concept helps determine how long it will take for a population to double?

Related terms

Exponential Function:

A mathematical function of the form $f(x) = a e^{bx}$, where $e$ is Euler’s number, and describes continuous and rapid increases or decreases.

Logarithmic Function:

$f(x) = \log_b(x)$, which is the inverse of an exponential function and grows more slowly than linear functions.

Carrying Capacity: The maximum population size that an environment can sustain indefinitely given available resources such as food and habitat.