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) =

More about this Exponential Decay Calculator

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

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