Half-life

Definition

Half-life is the time required for a quantity to reduce to half its initial value. It is commonly used in 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. In an exponential function describing decay, the quantity decreases by a factor of two every half-life period.
3. Half-life can be applied to various contexts such as radioactive decay, population decline, and chemical reactions.
4. To solve for half-life using logarithms, you can rearrange the formula $N(t) = N_0 e^{-kt}$ to find when $N(t) = \frac{N_0}{2}$.
5. Understanding half-life helps in solving problems related to exponential and logarithmic equations by providing a real-world application example.

Review Questions

• What is the mathematical relationship between the decay constant $k$ and the half-life?
• How do you determine the remaining quantity of a substance after multiple half-lives?
• Explain how logarithms are used to derive the half-life from an exponential decay equation.

Related terms

Exponential Decay: A process where a quantity decreases at a rate proportional to its current value. Represented by $N(t) = N_0 e^{-kt}$.

Decay Constant: The constant $k$ in exponential decay equations that determines the rate at which a quantity decreases.

Logarithm: $\log_b(x)$ is the exponent to which base $b$ must be raised to produce x. Commonly used in solving exponential equations.