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In a lab experiment, the decay of a radioactive isotope is being observed. At the beginning of the first day of the experiment the mass of the substance was 1300 grams and mass was decreasing by $14 \%$ per day. Determine the mass of the radioactive sample at the beginning of the 11th day of the experiment. Round to the nearest tenth (if necessary).
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Step 1 ：The problem is asking for the mass of the radioactive isotope at the beginning of the 11th day. Given that the mass of the substance was 1300 grams at the beginning and it was decreasing by 14% per day, we can use the formula for exponential decay to solve this problem.

Step 2 ：The formula for exponential decay is: \[ A = P(1 - r)^t \] where: - A is the amount of substance after time t, - P is the initial amount of the substance, - r is the rate of decay, and - t is the time.

Step 3 ：In this case, P = 1300 grams, r = 14% = 0.14, and t = 11 days. We can substitute these values into the formula and solve for A.

Step 4 ：Substituting the given values into the formula, we get: \[ A = 1300(1 - 0.14)^{11} \]

Step 5 ：Solving the above expression, we get A = 247.4

Step 6 ：Final Answer: The mass of the radioactive sample at the beginning of the 11th day of the experiment is \(\boxed{247.4}\) grams.