Exponential decay

Definition

Exponential decay describes a process where a quantity decreases at a rate proportional to its current value. Mathematically, it is expressed as $N(t) = N_0 e^{-kt}$, where $N_0$ is the initial quantity, $k$ is the decay constant, and $t$ is time.

5 Must Know Facts For Your Next Test

1. The formula for exponential decay is $N(t) = N_0 e^{-kt}$.
2. In exponential decay, the rate of decrease is proportional to the current amount.
3. The decay constant $k$ determines how quickly the quantity decreases over time.
4. A graph of an exponential decay function is a decreasing curve that approaches zero but never touches the x-axis.
5. Exponential decay can be used to model phenomena such as radioactive decay, population decline, and cooling of objects.

Review Questions

• What is the general form of an exponential decay function?
• How does the value of the decay constant $k$ affect the rate of decay?
• Describe how an exponential decay function appears on a graph.

Related terms

Exponential Function: A function in which an independent variable appears in the exponent and has the form $f(x) = ab^{x}$ or $f(x) = ae^{kx}$.

Half-Life: The time required for a quantity to reduce to half its initial value in a process undergoing exponential decay.

Decay Constant: $k$ in an exponential decay function; it represents the rate at which a quantity decreases over time.