Exponential decay

Definition

Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time. It is commonly modeled with the function $N(t) = N_0 e^{-kt}$, 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. In exponential decay, the quantity decreases at a rate proportional to its current value.
2. The decay constant $k$ determines how quickly the quantity decreases; larger values of $k$ result in faster decay.
3. The half-life of a substance undergoing exponential decay can be calculated using the formula $t_{1/2} = \frac{\ln(2)}{k}$.
4. Exponential decay can be integrated to find the total amount decayed over a specific time interval.
5. Common applications include radioactive decay, population decline, and cooling processes.

Review Questions

• What is the general formula for modeling exponential decay?
• How do you calculate the half-life of a decaying substance?
• Explain how integration is used in finding total quantity decayed over time.

Related terms

Exponential Growth: A process where a quantity increases at a rate proportional to its current value, often modeled as $N(t) = N_0 e^{kt}$ with similar variables as exponential decay but with positive $k$.

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

Decay Constant: $k$ in the exponential decay model; it quantifies the rate at which a substance or quantity decays.