Calculus II

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Exponential decay

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Calculus II

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.

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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.
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