To calculate the amount of the radioactive isotope remaining after 15 years, we can use the given formula:
\[ A(t) = 800 e^{-0.02825 t} \]
Substituting \( t = 15 \):
\[ A(15) = 800 e^{-0.02825 \times 15} \]
First, calculate the exponent:
\[ -0.02825 \times 15 = -0.42375 \]
Now calculate \( e^{-0.42375} \):
\[ e^{-0.42375} \approx 0.65458 \]
Now substitute this back into the equation for \( A(15) \):
\[ A(15) = 800 \times 0.65458 \approx 523.664 \]
Rounding to two decimal places, the amount remaining after 15 years is approximately:
\[ A(15) \approx 523.66 \text{ grams} \]
So the answer is:
523.66 grams