# How do you use the exponential decay formula?

I'll use an example from radioactive decay:

Taking natural logs of the decay equation we get:

I can use grams instead of number of atoms as they are proportional so the constant will cancel out.

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To use the exponential decay formula, which describes the decrease in value of a quantity over time, follow these steps:

- Identify the initial value of the quantity (denoted as ( P_0 )).
- Determine the rate of decay (denoted as ( r )) as a decimal or fraction.
- Find the time elapsed (denoted as ( t )) since the initial measurement.
- Use the exponential decay formula: ( P(t) = P_0 \times e^{-rt} ), where ( e ) is Euler's number (( \approx 2.71828 )).

Substitute the values of ( P_0 ), ( r ), and ( t ) into the formula and calculate ( P(t) ), which represents the quantity's value at time ( t ).

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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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