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To solve this problem, we use the concept of half-lives in exponential decay.

### Given:
- Initial amount of radioactive isotope = 120 grams
- After each half-life, the amount is halved.
- Number of half-lives = 5

### Solution:
For each half-life, the remaining amount is halved. So after \( n \) half-lives, the remaining quantity \( A \) can be calculated by:
\[
A = A_0 \times \left(\frac{1}{2}\right)^n
\]
where:
- \( A_0 \) is the initial amount (120 grams),
- \( n \) is the number of half-lives (5 in this case).

Substituting the values:
\[
A = 120 \times \left(\frac{1}{2}\right)^5
\]

### Calculating Step-by-Step:
1. \( \frac{1}{2}^5 = \frac{1}{32} \)
2. \( A = 120 \times \frac{1}{32} = \frac{120}{32} = 3.75 \)

So, after 5 half-lives, approximately **4 grams** of the isotope will be left (rounded to the nearest gram).

Would you like more details on exponential decay? 

Here are some related questions:
1. What is exponential decay, and how is it used in half-life problems?
2. How does doubling or halving time impact the decay formula?
3. Can this concept apply to fields outside radioactive decay?
4. What would happen to the remaining mass after 10 half-lives?
5. How can we calculate the decay rate if the half-life time is known?

**Tip:** Exponential functions are key in many natural processes, so understanding their behavior can help in various scientific fields.

The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 120 grams of a radioactive isotope, how much will be left after 5 half-lives?

Learn how to calculate the remaining mass of a radioactive isotope after 5 half-lives, starting with an initial amount of 120 grams. This problem uses the concept of exponential decay and half-life, ideal for high school students in Grades 9-12.

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