LaTeX
y(t)=y_0e^{-kt}Variables
- y_0: initial value
- k: decay constant
- t: elapsed time
How to use this formula
Solves a proportional decay law y′=−ky with positive rate k.
Important notes
- The model assumes the instantaneous decay rate is proportional to the current amount.
- Half-life is ln(2)/k.
Quick example
With y0=100 and k=0.1, y(10)=100e^{-1}.
Applicability, worked calculation, and verification
Assumptions and domain checks
- The model assumes the instantaneous decay rate is proportional to the current amount.
- State the domain together with any initial or boundary conditions, and confirm the regularity assumptions required by the method.
Worked example
With y0=100 and k=0.1, y(10)=100e^{-1}.
Common mistakes
- Before substituting values into Exponential Decay Model, map each variable to its definition and preserve every sign, exponent, subscript, and grouping mark.
- Do not present a general solution as the requested solution before applying all initial or boundary conditions.
Continue the workflow
Use Exponential Decay Model in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
y(t)=y_0e^{-kt}. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Digital Library of Mathematical FunctionsNational Institute of Standards and Technology — Definitions, notation, identities, and reference material for mathematical functions.
Frequently asked questions
What is the Exponential Decay Model used for?
Solves a proportional decay law y′=−ky with positive rate k.
Can I copy this formula as LaTeX?
Yes. Copy y(t)=y_0e^{-kt} or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.