Bismuth-210 is an isotope that radioactively decays by about 13% each day, meaning 13% of the remaining Bismuth-210 transforms into another atom (polonium-210 in this case) each day. If you begin with 269 mg of Bismuth-210, how much remains after 5 days?

After 5 days, what mg of Bismouth-210 remains?
Round your answer to the nearest hundredth as needed.

To solve this problem, we need to calculate the remaining mass of Bismuth-210 after 5 days using the decay rate formula for exponential decay:

\[
A(t) = A_0 \times (1 - r)^t
\]

Where:
- \( A(t) \) is the remaining amount of Bismuth-210 after \( t \) days.
- \( A_0 \) is the initial amount of Bismuth-210 (269 mg).
- \( r \) is the decay rate (13% per day, so \( r = 0.13 \)).
- \( t \) is the number of days (5 days).

Substituting the values:

\[
A(5) = 269 \times (1 - 0.13)^5
\]

Now let's compute the result.After 5 days, approximately 134.08 mg of Bismuth-210 remains.

Would you like further details or clarification? 

Here are 5 related questions to deepen your understanding:
1. What would be the remaining mass of Bismuth-210 after 10 days?
2. How long would it take for the amount of Bismuth-210 to decay to half its original value?
3. How would a different decay rate (e.g., 20% per day) affect the remaining mass after 5 days?
4. How do exponential decay formulas apply to other fields, such as economics or population growth?
5. What role does the decay constant play in radioactive decay processes?

**Tip:** Exponential decay processes often use the natural logarithm for continuous decay analysis, particularly when determining half-life.

Bismuth-210 is an isotope that radioactively decays by about 13% each day, meaning 13% of the remaining Bismuth-210 transforms into another atom (polonium-210 in this case) each day. If you begin with 269 mg of Bismuth-210, how much remains after 5 days? Round your answer to the nearest hundredth as needed.

Solve the problem of determining how much Bismuth-210 remains after 5 days of radioactive decay with a 13% daily decay rate. Using the exponential decay formula A(t) = A_0 × (1 - r)^t, we calculate the remaining mass of Bismuth-210 from an initial 269 mg, yielding approximately 134.08 mg after 5 days.

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