Calculus I

study guides for every class

that actually explain what's on your next test

Half-life

from class:

Calculus I

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.

congrats on reading the definition of half-life. now let's actually learn it.

ok, let's learn stuff

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

  • What is the relationship between the decay constant $k$ and half-life $t_{1/2}$?
  • How do you calculate the remaining quantity of a substance after one half-life has elapsed?
  • What role does integration play in understanding exponential decay models?

"Half-life" also found in:

Subjects (75)

© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.
Glossary
Guides