In the early 1960s, radioactive strontium-90 was released during atmospheric testing of nuclear weapons and got into the bones of people alive at the time. If the half-life of strontium-90 is 28 years, what fraction of the strontium-90 absorbed in 1964 remained in people's bones in 1996?

To determine what fraction of the radioactive strontium-90 absorbed in 1964 remained in people's bones in 1996, we can use the concept of radioactive decay, governed by the formula:

\[
N(t) = N_0 \left(\frac{1}{2}\right)^{\frac{t}{T_{\text{half}}}}
\]

Where:
- \( N(t) \) is the amount of substance remaining after time \( t \).
- \( N_0 \) is the initial amount of substance.
- \( T_{\text{half}} \) is the half-life of the substance.
- \( t \) is the elapsed time.

Given:
- The half-life (\( T_{\text{half}} \)) of strontium-90 is 28 years.
- The time elapsed from 1964 to 1996 is \( t = 1996 - 1964 = 32 \) years.

Now, we calculate the fraction of strontium-90 remaining after 32 years:

\[
\text{Fraction remaining} = \left(\frac{1}{2}\right)^{\frac{32}{28}} = \left(\frac{1}{2}\right)^{1.14}
\]

We'll now calculate this value.The fraction of strontium-90 remaining in people's bones in 1996, from what was absorbed in 1964, is approximately 0.453, or 45.3%.

Would you like further details or have any questions?

Here are 5 related questions for deeper understanding:
1. What is the general formula for radioactive decay?
2. How does the half-life of a substance influence its long-term presence in the environment?
3. What are the health impacts of long-term exposure to radioactive substances like strontium-90?
4. How is the half-life of a substance measured in a laboratory setting?
5. How do scientists use half-life data to track the environmental impact of nuclear tests?

**Tip:** When working with exponential decay, always ensure you understand how the base (like \(\frac{1}{2}\)) affects the rate at which the quantity decreases over time.

Learn how to calculate the fraction of radioactive strontium-90 remaining in people's bones from 1964 to 1996 using the half-life formula. This problem involves radioactive decay concepts and exponential functions, suitable for students in Grades 9-12.

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