Skeletons were found at a construction site in San Francisco

Skeletons were found at a construction site in San Francisco in 1989. The skeletons contained 88% of the expected amount of carbon-14 found in a living person. How old were the skeletons when they were found ? round answer to the nearest year.

Solution

For t=0, you get that A0 is the amount of carbon-14 found in a living person. Since you found 88% of it, then A = 0.88 A0... That means

0.88 = e^-0.000121t.

Take the natural logarithm (Ln) of the expression on both sides. Then

Ln (0.88) = Ln( e^-0.000121 t) but, from logarithm law\'s, this is equivalent to

Ln(0.88) = -0.000121 t Ln(e), but Ln(e) = 1. Solving for t, we get


t = Ln(0.88) / (-0.000121)
t = 1056.5

Now it depends in which scale is settled your time frame for the decay model (which usually is years).