https://file.aiquickdraw.com/mathbot/file/1728440935776krrvmzmu.jpg

The problem in the image asks about the final amount of a radioactive isotope after 5 half-lives, starting with 185 grams.

To solve this, we can use the formula for exponential decay related to half-life:

\[
A = A_0 \times \left( \frac{1}{2} \right)^n
\]

Where:
- \(A\) is the final amount of the isotope.
- \(A_0\) is the initial amount (185 grams).
- \(n\) is the number of half-lives (in this case, 5).

Let's calculate it:

\[
A = 185 \times \left( \frac{1}{2} \right)^5
\]
\[
A = 185 \times \frac{1}{32}
\]
\[
A = 5.78125 \text{ grams}
\]

Rounding to the nearest gram, the final amount is **6 grams**.

Would you like more details or have any questions?

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Here are 5 related questions:
1. What is the general equation for half-life decay?
2. How does increasing the number of half-lives affect the remaining amount of a substance?
3. What other factors, besides half-life, could affect radioactive decay?
4. How is the half-life of an isotope experimentally determined?
5. Can this formula be applied to real-world scenarios outside of radioactivity?

**Tip:** Half-life decay problems are exponential in nature. Understanding exponential growth and decay will help in many scientific and financial contexts.

The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 185 grams of a radioactive isotope, how much will be left after 5 half-lives?

Learn how to calculate the remaining amount of a radioactive isotope after 5 half-lives. Starting with 185 grams, find out how much is left using the exponential decay formula A = A_0 * (1/2)^n. This problem is suitable for students in Grades 9-12.

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