The mass of a radioactive substance follows a continuous exponential decay model. A sample of this radioactive substance has an initial mass of $339 \mathrm{~kg}$ and decreases continuously at a relative rate of $17 \%$ per day. Find the mass of the sample after three days.
Do not round any intermediate computations, and round your answer to the nearest tenth.

Step 1 ：The problem is asking for the mass of the radioactive substance after three days. The substance decreases continuously at a relative rate of 17% per day. This is an exponential decay problem. 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 2 ：In this case, \(P = 339 \, \text{kg}\), \(r = 0.17\) (17% expressed as a decimal), and \(t = 3 \, \text{days}\). We can substitute these values into the formula to find \(A\), the mass of the substance after three days.

Step 3 ：Substituting the given values into the formula, we get: \[ A = 339(1 - 0.17)^3 \]

Step 4 ：Solving the equation, we get: \[ A = 193.83579299999997 \]

Step 5 ：Rounding the result to the nearest tenth, we get: \[ A = 193.8 \]

Step 6 ：Final Answer: The mass of the sample after three days is approximately \(\boxed{193.8 \, \text{kg}}\).