Final answer:
Approximately 299.18 grams of the radioactive isotope remain after 30 years, calculated using the provided decay function and substituting 30 for the time variable.
Step-by-step explanation:
The question asks us to determine the amount of a radioactive isotope remaining after 30 years given the exponential decay function A(t) = 700e^(-0.02832t), where A(t) represents the amount after time t, given in years. To calculate the amount remaining, we substitute 30 for t:
A(30) = 700e^(-0.02832 × 30)
We can now evaluate this expression:
A(30) = 700 × e^(-0.8496)
Using a calculator to find e^-0.8496 (assuming an understanding of how to use the inverse logarithm function), we get approximately:
A(30) ≈ 700 × 0.4274
Thus, the approximate amount remaining after 30 years is:
A(30) ≈ 299.18 grams
Therefore, approximately 299.18 grams of the radioactive isotope remain after 30 years.