f we start with 50 grams of a radioactive substance that has a half-life of 835 years, how ong will it take for there to be 9.6 grams of the radioactive substance remaining? Round your answer to the nearest tenth of a year.

Step 1 ：Given that the initial amount of the radioactive substance, \(N_0\), is 50 grams, the final amount, \(N\), is 9.6 grams, and the half-life, \(h\), is 835 years.

Step 2 ：We can use the formula for exponential decay, which is \(N = N_0 \times (1/2)^{t/h}\), where \(t\) is the time.

Step 3 ：Rearranging this formula to solve for \(t\), we get \(t = h \times \log_{1/2}(N/N_0)\).

Step 4 ：Substituting the given values into the formula, we get \(t = 835 \times \log_{1/2}(9.6/50)\).

Step 5 ：Calculating the above expression, we find that \(t \approx 1988.0\).

Step 6 ：So, it will take approximately \(\boxed{1988.0}\) years for there to be 9.6 grams of the radioactive substance remaining.