Calculus II

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Half-life

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Calculus II

Definition

Half-life is the time required for a quantity to reduce to half of its initial value. It is commonly used in contexts involving exponential decay, such as radioactive decay or pharmacokinetics.

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5 Must Know Facts For Your Next Test

  1. The formula for calculating half-life in terms of the decay constant $\lambda$ is $t_{1/2} = \frac{\ln(2)}{\lambda}$.
  2. In exponential decay models, half-life remains constant regardless of the initial amount.
  3. Half-life can be derived using integration techniques from the differential equation $\frac{dy}{dt} = -\lambda y$.
  4. Understanding half-life is crucial for solving problems involving decay rates and predicting future amounts.
  5. The concept of half-life applies to various fields such as physics, chemistry, biology, and environmental science.

Review Questions

  • What is the relationship between the decay constant $\lambda$ and the half-life?
  • How would you use integration to derive the formula for half-life from a given exponential decay model?
  • If a substance has a known half-life, how can you determine the remaining quantity after a certain period?

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