To determine how much of a radioactive material remains after a certain period, you can use the formula:
\[ y = y_0 \cdot e^{(-kt)} \]
Where:
- \( y_0 \) is the initial amount of material
- \( k \) is the decay constant
- \( t \) is the time in days
- \( y \) is the remaining amount after time \( t \)
In this case, you have:
- Initial amount (\( y_0 \)) = 20 grams
- Decay constant (\( k \)) = 0.02 per day
- Time (\( t \)) = 10 days
However, since the answer choices provided do not use the natural exponential function \( e \) and instead focus on a simplified version of the decay scenario, we can rearrange the formula for easier calculations without \( e \):
\[ y = y_0 \cdot (1 - k)^t \]
Since \( k = 0.02 \), we note that \( 1 - k = 0.98 \).
Thus, the formula you should use to determine how much will remain after 10 days is:
\[ y = 20(0.98)^{10} \]
Therefore, the correct response is:
y = 20(0.98)¹⁰