# Exponential Decay Calculator

Instructions: Use this step-by-step Exponential Decay Calculator, to find the function that describe the exponential decay for the given parameters. You need to provide the initial value $$A_0$$, and the half life $$h$$ OR one value of the function at a future time.

Initial Value $$A_0$$ (number or fraction) =
Half-life (if known) =
Time in the future $$t_1$$ (if half-life not known) =
Value at $$t_1$$ (if half-life not known) =

A function $$f(t)$$ has exponential decay if it can be expressed as:

$f(t) = A_0 e^{-kt}$

The decay rate $$k$$ can be either provided, or you may need to calculate it. The initial value $$A_0$$ is typically provided.

There are basically two ways of giving information that you can use to compute $$k$$. For both ways you will need the initial value $$A_0$$. But that is not enough, and you will need one extra piece of information.

You can be either be provided with the corresponding half-life , OR you can be provided the value of the function at a certain future time.

For a more in depth analysis of exponential decay and its formula and properties, see this tutorial . Also you can use this exponential growth calculator for the case of exponential growth.

Also, it can be useful for you to graph