Determine the remaining activity of a radioactive atom after 5 seconds if the original activity is 75 mCi and the given transformation constant is 15% per second

To determine the remaining activity of a radioactive atom after a given time, we can use the exponential decay formula:

\[
A(t) = A_0 \cdot e^{-\lambda t}
\]

Where:
- \( A(t) \) is the remaining activity after time \( t \).
- \( A_0 \) is the initial activity.
- \( \lambda \) is the decay constant (transformation constant).
- \( t \) is the time.

Given:
- \( A_0 = 75 \, \text{mCi} \) (initial activity),
- \( \lambda = 0.15 \, \text{per second} \) (15% per second),
- \( t = 5 \, \text{seconds} \).

Now, let's calculate the remaining activity:

\[
A(5) = 75 \cdot e^{-0.15 \cdot 5}
\]

First, compute \( 0.15 \times 5 = 0.75 \). So, the formula becomes:

\[
A(5) = 75 \cdot e^{-0.75}
\]

Next, we evaluate \( e^{-0.75} \), which is approximately \( 0.472 \).

\[
A(5) = 75 \cdot 0.472 = 35.4 \, \text{mCi}
\]

Thus, the remaining activity after 5 seconds is approximately **35.4 mCi**.

Would you like more details on this? 

Here are 5 related questions to consider:
1. How does the transformation constant affect the decay rate?
2. What happens to the remaining activity if the transformation constant increases?
3. Can you derive the half-life from the transformation constant?
4. How would the remaining activity change if the initial activity were doubled?
5. What is the significance of the base \( e \) in exponential decay models?

**Tip:** Exponential decay is frequently used in both physics and biology to model processes like radioactive decay or population decrease over time.

Determine the remaining activity of a radioactive atom after 5 seconds if the original activity is 75 mCi and the given transformation constant is 15% per second.

Learn how to calculate the remaining activity of a radioactive atom after 5 seconds using exponential decay. The original activity is 75 mCi, with a 15% per second transformation constant. This solution is ideal for high school students in Grades 10-12, covering key concepts such as exponential decay and radioactive decay models.

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