To determine how much of the radioactive material will remain after 50 days, you can use the exponential decay formula:
\[ y = y_0 e^{-\lambda t} \]
where:
- \(y\) is the remaining quantity,
- \(y_0\) is the initial quantity,
- \(\lambda\) is the decay constant,
- \(t\) is the time in days.
In your scenario:
- \(y_0 = 100\) grams (initial amount),
- \(\lambda = 0.01\) per day (decay constant),
- \(t = 50\) days.
Plugging in the values:
\[ y = 100 e^{-0.01 \times 50} \]
However, since the responses provided do not use the natural exponential function, we can convert the decay constant to a form that uses a decay factor. The decay factor can be found as follows:
\[ \text{Decay factor} = e^{-\lambda} \approx 1 - \lambda \quad (\text{for small } \lambda) \]
For small decay constants, we can approximate \(e^{-0.01} \approx 0.99\), leading us to the equivalent equation:
\[ y \approx 100(0.99)^{50} \]
Thus, the correct equation from your responses to determine how much will remain after 50 days is:
\[ y = 100(0.99)^{50} \]
Therefore, the answer is:
\[ y=100(0.99)^{50} \]