Question
Question
A radioactive compound with mass 110 grams decays at a rate of
per hour. Which equation represents how many grams of the compound
will remain after 7 hours?
Answer
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A radioactive compound with mass 110 grams decays at a rate of
per hour. Which equation represents how many grams of the compound
will remain after 7 hours?
Answer
(© Watch Video Show Examples
Ask by Chan Byrd. in the United States
Mar 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The correct equation is
Solution
To determine the correct equation representing how many grams of the radioactive compound will remain after 7 hours, we need to consider the decay rate.
- The initial mass of the compound is
grams. - The decay rate is
per hour, which means that of the compound remains after each hour. - In decimal form,
is . - After
hours, the remaining mass can be expressed as: Substituting the values: - For
hours, the equation becomes:
Now, let’s evaluate the options provided:
-
- Incorrect, as this represents growth, not decay. -
- Correct, as it represents the remaining mass after decay. -
- Incorrect, as this represents a very small amount, not the remaining mass. -
- This is a valid representation but not in the exponential form.
Thus, the correct equation is:
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Simplify this solution Beyond the Answer
To understand radioactive decay, it’s vital to recognize that the compound decreases by a percentage, rather than increasing. Therefore, you should multiply by the percentage of remaining material, which is
In real-world applications, this concept is used in various fields like archaeology for radiocarbon dating, enabling scientists to estimate the ages of organic materials by measuring the remaining radioactive carbon isotopes. Similarly, in medicine, understanding the decay of radioactive isotopes is crucial for accurate dosage calculations in treatments like cancer radiotherapy.
