Question

A sample of a radioactive isotope had an initial mass of 110 mg in the year 1990 and decays exponentially over time. A measurement in the year 1993 found that the sample's mass had decayed to 90 mg. What would be the expected mass of the sample in the year 2002, to the nearest whole number?

Answer 1

To find the expected mass of the radioactive sample in the year 2002, we need to use the exponential decay formula. First, we determine the decay constant using the initial and final masses and the time. Then, we substitute the decay constant and the desired time into the formula to find the expected mass.

Step-by-step explanation:

To find the expected mass of the sample in the year 2002, we need to determine the decay constant and then use the exponential decay formula.

In this case, we can use the formula for exponential decay: mass = initial mass * e^(-decay constant * time)

Using the given information, we know that the initial mass is 110 mg and the final mass is 90 mg after a time of 3 years (1993-1990). We can rearrange the formula to solve for the decay constant: decay constant = ln(final mass/initial mass) / time. Substituting the values, we get decay constant = ln(90/110) / 3.

Now, we can use the decay constant to find the expected mass in the year 2002, which is 12 years after 1990. Substituting the values into the exponential decay formula: mass = 110 mg * e^(-decay constant * 12). Calculate this expression to find the expected mass in the year 2002.