Estimate the age of the skull if the half-life of carbon-14 is about 5600 years.

Question

Archaeologists believe the age of the skull to be the same age as the campfire. It is determined that only 2% of the original amount of carbon-14 remains in the burnt wood of the campfire.

Estimate the age of the skull if the half-life of carbon-14 is about 5600 years.

I have already tried the answer of 5600 * ln(0.02) / ln(0.5) and tried 5600*2*(ln(0.02) to get 7763; both are incorrect. I am not sure why that is incorrect if someone knows where I am going wrong that would be very helpful.

Answer 1

First get an equation.

This is exponential so the equation is in the form y = a*b^t

When t = 0 (present day), we have y = 2%

In 5600, the amount would half. Therefore, when t = 5600, y = 1%

We have two points (0, 2%) and (5600, 1%)

Plug those in to the equation:

0.02 = a*b⁰

0.01 = a * b⁵⁶⁰⁰

The first equation reduces to 0.02 = a

Solve for b, by plugging in a into the second equation

b = (1/2)^1/5600

Therefore, the equation is y =0.2(1/2)^t/5600

If you want to find the age of the school, find the time when the skull was fully in contact (when we had 100% of the skull)

So plug in 100% for y and solve for t