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We are tasked with modeling the radioactive decay of Iodine-125. The initial amount injected into the tumor is 0.5 grams, and the decay rate is 1.15% per day.

### Step 1: Write the Exponential Decay Model
The formula for exponential decay is given by:

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

Where:
- \( A(t) \) is the amount of substance remaining after time \( t \),
- \( A_0 \) is the initial amount of the substance,
- \( k \) is the decay constant, and
- \( t \) is the time in days.

Since the decay rate is 1.15% per day, we can express this as a rate of 0.0115. The exponential model becomes:

\[
A(t) = 0.5 \cdot e^{-0.0115t}
\]

### Step 2: Find the Amount Remaining After 60 Days
Now, we substitute \( t = 60 \) days into the formula:

\[
A(60) = 0.5 \cdot e^{-0.0115 \cdot 60}
\]

Let me compute this for you.After 60 days, approximately **0.2508 grams** of Iodine-125 will remain in the tumor.

Would you like a more detailed breakdown or have any questions?

Here are 5 follow-up questions to expand on the topic:

1. How does the half-life of Iodine-125 relate to this decay model?
2. What happens to the decay model if the decay rate changes over time?
3. How would you calculate the decay constant \( k \) if given the half-life instead of the decay rate?
4. What is the relationship between exponential decay and half-life in radioactive substances?
5. How can you use this model to predict when less than 0.1 grams will remain?

**Tip:** In any exponential decay problem, identifying the decay constant is key to modeling how fast the substance decreases over time.

A tumor is injected with 0.5 grams of Iodine-125, which has a decay rate of 1.15% per day. Write an exponential model representing the amount of Iodine-125 remaining in the tumor after t days. Then use the formula to find the amount of Iodine-125 that would remain in the tumor after 60 days.

Learn how to model the decay of Iodine-125 in a tumor with a decay rate of 1.15% per day. This problem uses the exponential decay formula to calculate the amount of Iodine-125 remaining after 60 days. Suitable for students in Grades 11-12.

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