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.
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Exponential growth of a population occurs when the growth rate is proportional to the current population size, leading to a rapid increase.
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.
Logistic growth models are used when there are limiting factors that slow down population growth as it approaches a maximum sustainable size (carrying capacity).
The integral of an exponential function can be used to calculate total population over a period of time.
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.