The table shows the exponential relationship between the number of grams of a radioactive sample, y, and the number of years, x, since the sample was first measured.
Radioactive Decay
Number of Years, x Amount of Sample, y (grams)
1 10.52
3 8.08
7 4.77
8 4.18
Which measurement is the best estimate of the number of grams of the sample remaining after 5 years?
Option A.
6.21 g
Option B.
4.77 g
Option C.
5.64 g
Option D.
5.36 g
To estimate the number of grams of the sample remaining after 5 years, we can examine the trend in the data.
From the table, we can observe that as the number of years increases, the amount of the sample decreases. This indicates that the sample is undergoing radioactive decay.
Since the years are increasing in a non-linear pattern, we cannot simply find the average of the amounts of the sample at 3 and 7 years (which would be (8.08 + 4.77)/2 = 6.43 g).
To estimate the amount remaining after 5 years, we can look for the closest years with measured amounts to 5 years. In this case, the closest years are 3 years and 7 years.
From the table, at 3 years the sample has 8.08 g and at 7 years the sample has 4.77 g. The trend suggests that the amount of the sample decreases as the number of years increases, so it is likely that the amount remaining after 5 years (between 3 and 7 years) will be closer to 4.77 g.
Therefore, the best estimate of the number of grams of the sample remaining after 5 years is Option B. 4.77 g.