A biologist has a 987-gram sample of a radioactive substance. Find the mass of the sample after two hours if it decreases according to a continuous exponential decay model, at a relative rate of $12 \%$ per hour.
Español
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 sample after two hours given that it decreases according to a continuous exponential decay model, at a relative rate of 12% per hour. The formula for continuous exponential decay is given by: \[ P(t) = P_0 * e^{(-rt)} \] where: \( P(t) \) is the final amount, \( P_0 \) is the initial amount, \( r \) is the rate of decay, and \( t \) is the time.

Step 2 ：In this case, \( P_0 = 987 \) grams, \( r = 0.12 \) per hour, and \( t = 2 \) hours. We can substitute these values into the formula to find the final amount.

Step 3 ：Substituting the given values into the formula, we get: \[ P(t) = 987 * e^{(-0.12*2)} \]

Step 4 ：Solving the above expression, we find that \( P(t) = 776.4 \)

Step 5 ：Final Answer: The mass of the sample after two hours is \(\boxed{776.4}\) grams.