Question

A biologist has a 597-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 12% per hour.

Answer 1

To find the mass of the sample after four hours of continuous exponential decay at a relative rate of 12% per hour, we can use the formula Final Mass = Initial Mass * e^(-rt). Substituting the values given, the final mass is approximately 472.5 g.

Step-by-step explanation:

To find the mass of the sample after four hours, we can use the formula for exponential decay:

Final Mass = Initial Mass × e-rt

Where:
r = relative rate of decay (in this case, 0.12 or 12% per hour)
t = time (in this case, 4 hours)

Substituting the given values:

Final Mass = 597 g × e-0.12 × 4

Using a calculator, this comes out to be approximately 472.5 g.