key term - Half-life

Definition

Half-life is the time required for a quantity to reduce to half its initial value. It is commonly used in the context of exponential decay processes.

5 Must Know Facts For Your Next Test

1. The formula for half-life in exponential decay is $t_{1/2} = \frac{\ln(2)}{k}$, where $k$ is the decay constant.
2. Half-life is independent of the initial amount of substance present.
3. In a continuous exponential decay model, the remaining quantity after time $t$ can be calculated using $N(t) = N_0 e^{-kt}$.
4. For a function describing population or material decay, integrating from 0 to infinity will yield the total area under the curve, representing the overall quantity over time.
5. Understanding half-life helps in solving problems involving radioactive decay, pharmacokinetics, and other natural processes modeled by differential equations.

Review Questions

Related terms

Exponential Decay: A process where quantities decrease at a rate proportional to their current value.

$e$ (Euler's Number): An irrational number approximately equal to 2.71828, which serves as the base for natural logarithms and is used in modeling continuous growth or decay.

$\ln(x)$ (Natural Logarithm): $\ln(x)$ represents the logarithm of $x$ with base $e$, commonly used in solving equations involving exponential growth or decay.