Exponential Growth and Decay Models

Flashcards covering key vocabulary related to exponential growth and decay, including definitions and relevant concepts.

Exponential Growth

A process that increases quantity over time, often characterized as doubling or growing by a constant percentage.

Decay Factor

In decay models, the ratio by which a quantity decreases, for example, in the equation f(t) = 36,500 (0.68)^t, 0.68 is the decay factor.

Initial Value

The starting amount before any growth or decay has taken place, such as the initial value of a car in the model f(t) = 36,500 (0.68)^t.

Half-life

The time required for a quantity to reduce to half its initial amount.

Value Appreciation Formula

The formula to calculate the future value of an asset, represented as V = P(1 + r)^t, where P is the principal, r is the rate of return, and t is the time.

Invasive Species

Non-native species whose introduction causes or is likely to cause economic or environmental harm.

Function Notation

A way to denote functions, exemplified in V(t) = 240,000 (1.06)^t, to represent the home value based on time.

Cost Function

A mathematical function describing the cost involved in performing an operation based on other variables, such as time or units.

Growth Model

An equation that represents how size increases over time, such as Y = initial amount * (growth factor)^time.

Diminishing Returns

A point at which the incremental gains from an investment or action will begin to decrease.