Questions: The mass of a radioactive substance follows a continuous exponential decay model. A sample of this radioactive substance has an initial mass of 1274 kg an decreases continuously at a relative rate of 7% 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. kg

Find the mass of the radioactive substance after three days.

Identify the initial mass and decay rate.

The initial mass \( m_0 = 1274 \, \text{kg} \) and the decay rate \( r = 0.07 \) per day.

Apply the exponential decay formula.

The formula for exponential decay is given by:

\[ m(t) = m_0 \cdot e^{-rt} \]

Substituting the known values:

\[ m(3) = 1274 \cdot e^{-0.07 \cdot 3} \]

Calculate the final mass.

Calculating the exponent:

\[ -0.07 \cdot 3 = -0.21 \]

Now, substituting back into the formula:

\[ m(3) = 1274 \cdot e^{-0.21} \approx 1274 \cdot 0.81093 \approx 1032.6843293660183 \]

Rounding to the nearest tenth gives:

\[ m(3) \approx 1032.7 \, \text{kg} \]

The mass of the sample after three days is \( \boxed{1032.7} \) kg.

The mass of the sample after three days is \( \boxed{1032.7} \) kg.