# Exponential decay

A quantity is subject to **exponential decay** if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where *N* is the quantity and *λ* (lambda) is a positive rate called the **exponential decay constant**:

The solution to this equation (see derivation below) is:

where *N*(*t*) is the quantity at time *t*, *N*_{0} = *N*(0) is the initial quantity, that is, the quantity at time *t* = 0, and the constant *λ* is called the **decay constant**, **disintegration constant**,[1] **rate constant**,[2] or **transformation constant**.[3]