Question

A biologist has a 595-gram sample of a radioactive substance. Find the mass of the sample after six hours if it decreases according to a continuous exponential

decay model, at a relative rate of 11% per hour.
Do not round any intermediate computations, and round your answer to the nearest tenth.
grams

Answer 1

Therefore, the mass of the sample after six hours is approximately 339.8 grams to the nearest tenth gram.

Explanation:

The decay of the radioactive substance can be modeled using the formula:

m(t) = m₀ * e^(-kt)

where:

m₀ = initial mass of the substance (595 grams)

t = time elapsed (6 hours)

k = decay constant (which we need to find)

m(t) = mass of the substance at time t (what we are looking for)

The relative rate of decay per hour is 11%, which means that the decay constant is:

k = ln(1 - 0.11) / 1 = -0.1178 per hour

where ln is the natural logarithm.

Substituting the given values into the formula, we get:

m(6) = 595 * e^(-0.1178 * 6) = 339.8 grams

Therefore, the mass of the sample after six hours is approximately 339.8 grams to the nearest tenth gram.