# How to calculate age using carbon dating

CARBON-14 IS ABSORBED (Figure 1b): Plants absorb this carbon-14 during photosynthesis.

When animals eat the plants, the carbon-14 enters their bodies.

(Since this is a decay problem, I expect the constant to be negative.

Rb)—are not being formed on earth, as far as we know.

Thus it appears that God probably created those elements when He made the original earth.

Carbon-14 can yield dates of only “thousands of years” before it all breaks down.

Although many people think radiocarbon dating is used to date rocks, it is limited to dating things that contain the element carbon and were once alive (like fossils).

If we assume Carbon-14 decays continuously, then $$C(t) = C_0e^,$$ where $C_0$ is the initial size of the sample. Since it takes 5,700 years for a sample to decay to half its size, we know $$\frac C_0 = C_0e^,$$ which means $$\frac = e^,$$ so the value of $C_0$ is irrelevant.

Now, take the logarithm of both sides to get $$-0.693 = -5700k,$$ from which we can derive  k \approx 1.22 \cdot 10^.

CARBON-14 IS CREATED (Figure 1a): When cosmic rays bombard the earth’s atmosphere, they produce neutrons.

These excited neutrons then collide with nitrogen atoms in the atmosphere, changing them into radioactive carbon-14 atoms.

But while the difficulties of single life may be intractable, the challenge of determining the age of prehistoric artifacts and fossils is greatly aided by measuring certain radioactive isotopes.

Until this century, relative dating was the only technique for identifying the age of a truly ancient object.

By examining the object's relation to layers of deposits in the area, and by comparing the object to others found at the site, archaeologists can estimate when the object arrived at the site.