Answer:
Third choice:
Explanation:
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<u>1. Data:</u>
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- Function:
- Cobalt-60's half-life: 5.3 years
- Initial mass of cobalt-60: 50 mg
<u>2. Unknown: </u>
<u />
- equation for the mass of cobalt-60 remaining after 10 years = ?
- mass remaining =?
<u>3. Solution</u>
<em>Half-life</em> is the time it takes a sample to decay to half of its initial amount. It is considered constant. Hence, when one half-life passes, the sample has decayed to 50% of the original amount; when two half-lives pass, the sample has decayed to (1/2)×(1/2) = 1/4 = 25%; when three half-lives have elapsed, the sample has decayed to (1/2)³ = 1/8 = 12.5% of its original amount, and so on.
Then, the amound of a sample remaining is calculated as the original amount times (1/2) raised to the number of half-lives elapsed, which is what the given function, models.
You just must substitute the data into the function to get the answer to the question:
Where, 50 is the original mass of 50g, 0.5 is equal to 1/2, and 10/5.3 gives the number of half-lives (the number of times that 5.3 years is contained in 10 years).
<u>Simplifying:</u>
Which corresponds to the third choice of the list.
<u>Computing:</u>
Which also corresponds to the third choice.
