Pregunta
There was a sample of 900 milligrams of a radioactive substance to start a study. Since then, the sample has decayed by
each year.
Let
be the number of years since the start of the study. Let
be the mass of the sample in milligrams.
Write an exponential function showing the relationship between
and
.
.
Let
Write an exponential function showing the relationship between
.
Ask by Harmon Byrd. in the United States
Mar 15,2025
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The relationship between
and
is
.
Solución

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Como
Beyond the Answer
To model the decay of the radioactive substance, we can use the exponential decay formula:
where
is the initial amount,
is the decay rate, and
is the time in years. Here,
mg and
(7.4% as a decimal). Plugging these values in gives us:
This function now describes the relationship between the mass of the sample and the time in years.
Just a fun fact: This type of decay is often used when discussing half-lives, which indicate how long it takes for half of the substance to decay. For this sample, you can calculate the half-life using the formula:
Calculating that out gives you an idea of how quickly or slowly the substance would decay to half its original mass!

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