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To solve this problem, we need to use the exponential decay formula:

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

where:
- \( A(t) \) is the amount of substance remaining after time \( t \),
- \( A_0 = 0.5 \) grams is the initial amount of Iodine-125,
- \( k \) is the decay constant (which we will calculate from the given decay rate),
- \( t \) is the time in days.

### Step 1: Determine the decay constant \( k \)
The problem states that Iodine-125 decays at a rate of 1.15% per day. This means that the decay rate is \( 0.0115 \) per day. Since the rate is given as a percentage of the current amount, the decay constant \( k \) is the same as the given decay rate:

\[
k = 0.0115
\]

### Step 2: Write the exponential decay model
The exponential model for this problem becomes:

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

### Step 3: Calculate the remaining amount after 60 days
Substitute \( t = 60 \) into the model to find the amount of Iodine-125 remaining after 60 days:

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

Now let's calculate this value.

\[
A(60) = 0.5 \cdot e^{-0.69}
\]

Let me compute the final value.After 60 days, the remaining amount of Iodine-125 in the tumor is approximately **0.2508 grams**.

### Final exponential model:
\[
A(t) = 0.5 \cdot e^{-0.0115t}
\]

### Amount after 60 days:
\[
A(60) \approx 0.2508 \, \text{grams}
\]

Would you like further clarification, or do you have any questions?

Here are 5 related questions for further exploration:
1. How would the model change if the decay rate were 2% instead of 1.15%?
2. How long would it take for the amount of Iodine-125 to reduce to 0.1 grams?
3. What is the half-life of Iodine-125 based on the given decay rate?
4. Can you derive a general formula to find the remaining amount after any number of days?
5. How does the exponential decay model apply to other radioactive substances?

**Tip:** When dealing with exponential decay problems, understanding the relationship between the decay constant and half-life can be very useful.

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 exponential decay of Iodine-125 in a tumor with a decay rate of 1.15% per day. The problem involves finding the remaining amount of Iodine-125 after 60 days. This problem covers key concepts in exponential decay and radioactive decay, suitable for high school students.

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