Sure, let's construct a radioactive decay graph for an isotope with a half-life of 75 thousand years.
On the x-axis, we'll have time in thousands of years, and on the y-axis, we'll have the percentage of the original isotope remaining.
Starting with 100% of the original isotope at time zero, we'll plot the points on the graph:
Time (in thousands of years) | Percentage of Isotope Remaining
----------------------------------------------------------
0 | 100%
75 | 50%
150 | 25%
225 | 12.5%
300 | 6.25%
375 | 3.125%
450 | 1.5625%
525 | 0.78125%
Now, to estimate the age of a sample that contains 40% of the original isotope, we can draw a horizontal line at 40% on the y-axis and see where it intersects with the decay curve.
Based on the graph, it appears that the intersection occurs at around 155 thousand years (between 150 and 225 thousand years).
Therefore, the estimated age of the sample containing 40% of the original isotope is approximately 155 thousand years.
Remember, radioactive decay graphs can give us estimates, but actual measurements may vary. ️