---
title: "Exponential Decay — AP Calculus Definition & Exam Guide"
description: "Exponential decay models quantities shrinking at a rate proportional to their size, dy/dt = ky with k < 0, solved by y = y₀e^(kt). Core to AP Calc Unit 7."
canonical: "https://fiveable.me/ap-calc/key-terms/exponential-decay"
type: "key-term"
subject: "AP Calculus AB/BC"
---

# Exponential Decay — AP Calculus Definition & Exam Guide

## Definition

Exponential decay refers to the process by which something decreases rapidly initially and then continues to decrease over time, following an exponential pattern. In mathematics, it can be represented by an exponential function with a negative exponent.

## Review

### Related Terms

- [Exponential Growth](/ap-calc/key-terms/exponential-growth): Exponential growth is the opposite of exponential decay, where something increases rapidly initially and then continues to grow over time according to an exponential pattern.
- Half-Life: The half-life is the amount of time it takes for half of a substance or quantity to decay or decrease by half through exponential decay.
- Decay Constant: The decay constant represents how quickly something decays or decreases over time in an exponential decay model.