The half-life of strontium-90 is approximately 29 years. How much of a 500 g sample of strontium- 90 will remain after 58 years? Remaining Amount $$ =[?](1-\square) $$

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To determine how much of a 500 g sample of strontium-90 ($$ \text{Sr-90} $$) will remain after 58 years, we can use the concept of **half-life**. The half-life is the time required for half of the radioactive substance to decay.

### Given:
- **Half-life of Sr-90 ($$ t_{1/2} $$)**: 29 years
- **Initial amount ($$ A_0 $$)**: 500 g
- **Time elapsed ($$ t $$)**: 58 years

### Step-by-Step Calculation:

1. **Determine the Number of Half-Lives ($$ n $$)**:
   
   $$
   n = \frac{t}{t_{1/2}} = \frac{58 \text{ years}}{29 \text{ years}} = 2
   $$
   
   So, 2 half-lives have passed.

2. **Calculate the Remaining Amount ($$ A $$)**:
   
   The formula for the remaining amount after $$ n $$ half-lives is:
   
   $$
   A = A_0 \left( \frac{1}{2} \right)^n
   $$
   
   Plugging in the values:
   
   $$
   A = 500 \text{ g} \times \left( \frac{1}{2} \right)^2 = 500 \text{ g} \times \frac{1}{4} = 125 \text{ g}
   $$
   
### Final Answer:
After 58 years, **125 grams** of the original 500 g sample of strontium-90 will remain.

### Formula Representation:
If you'd like to express this using the formula structure you provided:

$$
\text{Remaining Amount} = 500 \left( \frac{1}{2} \right)^2 = 125 \text{ g}
$$

Where:
- **Initial Amount** = 500 g
- **Decay Factor** = $$ \left( \frac{1}{2} \right)^2 $$ because 2 half-lives have elapsed.

### Summary:
- **Initial Amount**: 500 g
- **Time Elapsed**: 2 half-lives (58 years)
- **Remaining Amount**: 125 g

After 58 years, 125 g of the original 500 g of strontium-90 remains.
After 58 years, 125 grams of the original 500 grams of strontium-90 will remain.

The half-life of strontium-90 is approximately 29 years. How much of a 500 g sample of strontium- 90 will remain after 58 years? Remaining Amount \( =[?](1-\square) \)

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