To find the amount of the radioactive isotope remaining after 15 years, we can use the formula provided:
\[ A(t) = 400 e^{-0.02833 t} \]
Substituting \( t = 15 \) into the equation:
\[ A(15) = 400 e^{-0.02833 \times 15} \]
First, calculate the exponent:
\[ -0.02833 \times 15 = -0.42495 \]
Now substitute this back into the equation:
\[ A(15) = 400 e^{-0.42495} \]
Next, we can calculate \( e^{-0.42495} \):
\[ e^{-0.42495} \approx 0.6533 \quad (\text{using a scientific calculator}) \]
Now, we can continue:
\[ A(15) = 400 \times 0.6533 \approx 261.32 \]
So, the amount of the radioactive isotope remaining after 15 years is approximately:
\[ \boxed{261.32} \text{ grams} \]