Question

a biologist has a 1142-gram sample of a radioactive substance. find the mass of the sample after three hours if it decreases according to a continuous exponential decay model, at a relative rate of 7% per hour. do not round any intermediate computations, and round your answer to the nearest tenth.

Answer 1

To calculate the remaining mass of a radioactive sample after three hours with a relative decay rate of 7% per hour, we use the exponential decay model, plug in the values, and then round the result to the nearest tenth.

Step-by-step explanation:

To find the mass of a radioactive sample after a certain period, we can use the exponential decay model equation:

M(t) = M_0 e(-rt)

Where:

• M(t) is the remaining mass after time t,
• M_0 is the initial mass,
• r is the decay rate per unit of time,
• t is the time in the same units as the decay rate.

In this question:

• M_0 = 1142 grams,
• r = 7% per hour, or 0.07 per hour,
• t = 3 hours.

Plugging in the values:

M(3) = 1142 e(-0.07 × 3)

After calculating this expression, we should round the result to the nearest tenth to get the final answer.

m(3) = 809.6 grams (rounded to the nearest tenth)