# 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.

InitialValue $$A_0$$ (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

In case you have any suggestion, or if you would like to report a broken solver/calculator, please do not hesitate to contact us.