To find the expected mass of the sample in the year 2017, we can use the concept of radioactive decay. The expected mass can be calculated using the formula for radioactive decay and the given information about the initial mass and the decayed mass.
The expected mass of the sample in the year 2017 would be approximately 330 mg, to the nearest whole number.
To find the expected mass of the sample in the year 2017, we can use the concept of radioactive decay. Since the sample decays exponentially, we can use the formula:
Current mass = Initial mass * (1/2)^(t / half-life)
Where t is the time elapsed and half-life is the time it takes for half of the sample to decay.
First, we need to find the time elapsed from 2005 to 2012, which is 7 years. Then, we can find the half-life of the isotope or use the given information. Let's assume the half-life is 10 years for this example.
Plugging in the values:
Current mass = 450 mg * (1/2)^(7 / 10) = 310 mg
We can rearrange the formula to solve for the time t:
t = - (half-life) * log(Current mass / Initial mass) / log(1/2)
Plugging in the values:
t = - 10 * log(310 / 450) / log(1/2) = 3.4 years
Therefore, the time from 2012 to 2017 is 3.4 years. Adding this to the previous time, we get a total time of 10.4 years.
Now, we can use the formula to find the expected mass in 2017:
Expected mass = Initial mass * (1/2)^(10.4 / 10) = 450 mg * (1/2)^(10.4 / 10) = 330 mg
Therefore, the expected mass of the sample in the year 2017 would be approximately 330 mg, to the nearest whole number.