Question

A fossil contains 19% of the carbon-14 that the organism contained when it was alive. Graphically estimate its age. Use 5700 years for the half-life of carbon-14.

The fossil is approximately _years old.
(Round to the nearest integer as needed.)

Answer 1

In this specific question, the first thing you should do is to figure out what k is. You can do this by using the fact that the half life of carbon-14 is 5700 years. To find k set up your equation as follows:

.5=e^5700k

To figure out k here take the natural log of both sides:

ln(.5)=5700k

Then solve for k:

k=ln(.5)/5700 ~~ -1.216*10^-4

Now that we know what k is, we can go back to the original question and plug in everything we know! Our new equation should look like this:

.04=e^((ln(.5)/5700)t)

Solving for t works the same as solving for k, take the natural log of both sides:

ln(.04)=(ln(.5)/5700)t

Then solve for t:

t=ln(.04)/(ln(.5)/5700) ~~ 26469.98 years