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Answer:
It will take about 109.3 seconds for nine grams of the element to decay to 0.72 grams.
Step-by-step explanation:
We can write a half-life function to model our function.
A half-life function has the form:
Where <em>A₀</em> is the initial amount, <em>t</em> is the time that has passes (in this case seconds), <em>d</em> is the half-life, and <em>A</em> is the amount after <em>t</em> seconds.
Since the half-life of the element is 30 seconds, <em>d</em> = 30. Our initial sample has nine grams, so <em>A₀</em> is 9. Substitute:
We want to find the time it will take for the element to decay to 0.72 grams. So, we can let <em>A</em> = 0.72 and solve for <em>t: </em>
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Divide both sides by 9:
We can take the natural log of both sides:
By logarithm properties:
Solve for <em>t: </em>
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So, it will take about 109.3 seconds for nine grams of the element to decay to 0.72 grams.