To determine how much of a radioactive material will remain after a certain time is typically modeled with the equation:
\[ y = y_0 e^{-\lambda t} \]
where:
- \(y\) is the amount of material remaining,
- \(y_0\) is the initial amount of material (500 grams in this case),
- \(\lambda\) is the decay constant (0.04 per hour in this case),
- \(t\) is the time in hours (3 hours in this case),
- \(e\) is the base of the natural logarithm.
Using your specific values, the equation would be:
\[ y = 500 e^{-0.04 \cdot 3} \]
So this is the equation you would use to determine how much will remain after 3 hours. For the options given, none of them correctly represent the exponential decay equation, so you may want to check if there are any typographical errors.
If you intended to represent the decay as a function of time and using a base decay factor, the alternative accurate model could be:
\[ y = 500(1 - \text{decay factor})^t \]
However, the original exponential decay formula is the most appropriate.