Here we have to apply the reasoning of problem 4 in several stages. If a bone has 8 micrograms of ¹⁴C when the person died, it will have 4 micrograms after one half-life (6000 years). After another 6000 years it will have 2 micrograms (half of the 4 micrograms). After another 6000 years the 2 micrograms will be reduced to half; only 1 microgram remains.

So altogether 18,000 years elapse as the initial 8 micrograms is reduced to 1 microgram. If we see 1 microgram today, the person died 18,000 years ago.

Note it is not difficult to follow this reasoning if the number we see today is 4, 2, or 1 micrograms (or we could do it with .5, .25 etc.). What if the present observation is some other number, say 3 micrograms, or 1.76 micrograms? One way to answer this question is to draw a rough graph of the remaining carbon vs. the time, using 3 or 4 points that can be calculated as above. Draw a smooth curve through the points, and use the curve to find elapsed time for any given quantity of carbon.