What is Exponential Decay?

Exponential decay is a mathematical concept that describes the process where a quantity decreases over time at a rate proportional to its current value. In other words, the quantity’s decrease rate is directly proportional to its current size. This leads to a rapid decrease initially, followed by a gradual decrease of decay as the quantity gets smaller.

General form of an exponentially decaying function is:

[Tex]y = y_0 \times e^{-kt}[/Tex]

Where:

• y is the value of the quantity at time t.
• y₀ is the initial value of the quantity (at t = 0).
• k is the decay constant, which determines the rate of decay.
• e is the base of the natural logarithm (approximately equal to 2.71828).

Exponential decay is commonly observed in various natural phenomena, such as radioactive decay, population decline, decay of electrical charge in a capacitor, and the decay of certain types of financial investments.

Examples like a cooling cup of coffee or a fading yell in a hallway demonstrate exponential decay is a concept in math where a quantity decreases over time at a slower rate than linear decay which decreases at a constant rate. This idea has many applications and affects our environment in surprising ways.