# How do you find the equation of exponential decay?

Exponential decay and growth occurs widely in nature so I will use radioactive decay as an example.

When an atom decays it is a random, chance event. The number of atoms decaying per second depends only on the number of undecayed atoms N.

So we can write:

Rate of decay:

Rearranging gives:

Integrating both sides:

So

So

So

So

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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