To determine the amount of radioactive material remaining after a certain time, you can use the exponential decay formula:
\[ y = y_0 e^{-\lambda t} \]
where:
- \( y \) is the amount remaining after time \( t \),
- \( y_0 \) is the initial amount,
- \( \lambda \) is the decay constant, and
- \( t \) is the time in days.
In this case, you have:
- The initial amount \( y_0 = 20 \) grams,
- The decay constant \( \lambda = 0.02 \) per day, and
- The time \( t = 10 \) days.
Using the decay formula, we can rewrite it using exponential decay in terms of the decay factor, which is \( (1 - \lambda) \):
\[ y = y_0 (1 - \lambda)^t = y_0 (0.98)^t \]
Substituting in the values:
\[ y = 20 (0.98)^{10} \]
Thus, the correct formula to determine how much material will remain after 10 days is:
D. \( y = 20(0.98)^{10} \).
The options provided might contain a typographical error since none of them match the standard form above. However, from the context, D is the closest correct form to represent the remaining amount after the decay over 10 days.
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