How much of a radioactive kind of bismuth will be left after 8 minutes if the half-life is 2 minutes and you start with 79,360 grams?

The amount of a radioactive substance left after a certain time can be calculated using the formula for exponential decay:

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

Where:
- \( A(t) \) is the amount of substance left after time \( t \),
- \( A_0 \) is the initial amount of the substance (79,360 grams),
- \( t \) is the total time (8 minutes),
- \( T_{\frac{1}{2}} \) is the half-life of the substance (2 minutes).

Now, substituting the values:

\[
A(8) = 79,360 \times \left( \frac{1}{2} \right)^{\frac{8}{2}} = 79,360 \times \left( \frac{1}{2} \right)^4
\]

\[
A(8) = 79,360 \times \frac{1}{16} = 4,960 \text{ grams}
\]

Thus, after 8 minutes, **4,960 grams** of the radioactive bismuth will be left.

Would you like further details or clarifications on this? 

Here are 5 questions that expand on this topic:
1. How does the decay constant relate to the half-life in radioactive decay?
2. What is the general form of the exponential decay equation?
3. How can you use logarithms to find the time taken for a substance to decay to a specific amount?
4. How does the half-life concept apply in fields other than radioactivity, such as pharmacology?
5. What happens to the particles of the substance that decay?

**Tip**: When dealing with half-life problems, always ensure the time elapsed is expressed in terms of the half-life units.

Find out how much of a radioactive kind of bismuth remains after 8 minutes if the half-life is 2 minutes and the initial amount is 79,360 grams. This problem involves exponential decay and is suitable for students in Grades 9-12.

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