Finding the final amount in a word problem on continuous... A biologist has a 1831 -gram sample of a radioactive substance. Find the mass of the sample after four hours if it decreases according to a continuous exponential decay model, at a relative rate of \( 13 \% \) per hour. Do not round any intermediate computations, and round your answer to the nearest tenth. \( \square \) grams

To solve the problem, we can use the formula for continuous exponential decay, which is given by: \[ A(t) = A_0 e^{(-rt)} \] where: - \( A(t) \) is the amount remaining after time \( t \), - \( A_0 \) is the initial amount (1831 grams), - \( r \) is the decay rate (0.13 for 13%), - \( t \) is the time in hours (4 hours), - \( e \) is the base of the natural logarithm (approximately equal to 2.71828). Plugging the numbers into the formula: \[ A(4) = 1831 e^{(-0.13 \times 4)} \] Calculate the exponent: \[ -0.13 \times 4 = -0.52 \] Now compute \( e^{-0.52} \): \[ e^{-0.52} \approx 0.595 \] Substituting back into the equation: \[ A(4) = 1831 \times 0.595 \approx 1095.145 \] Rounding to the nearest tenth, the mass of the sample after four hours is \( \boxed{1095.1} \) grams.