# Carbon dating calculus

Radiocarbon *dating* uses isotopes of the element *carbon*. Cosmic rays – high energy particles from beyond the solar system – bombard Earth’s upper atmosphere continually, in the process creating the unstable *carbon*-14. Because it’s unstable, *carbon*-14 will eventually decay back to *carbon*-12 isotopes.

Because the cosmic ray bombardment is fairly constant, there’s a near-constant level of *carbon*-14 to *carbon*-12 ratio in Earth’s atmosphere.

Organisms at the base of the food chain that photosynthesize – for example, plants and algae – use the **carbon** in Earth’s atmosphere.

They have the same ratio of *carbon*-14 to *carbon*-12 as the atmosphere, and this same ratio is then carried up the food chain all the way to apex predators, like sharks.

When an organism dies it ceases to replenish **carbon** in its tissues and the decay of **carbon** 14 to nitrogen 14 changes the ratio of **carbon** 12 to **carbon** 14.

Experts can compare the ratio of **carbon** 12 to **carbon** 14 in dead material to the ratio when the organism was alive to estimate the date of its death.

Atoms of the same element that have different numbers of neutrons are called isotopes. Most **carbon** on Earth exists as the very stable isotope **carbon**-12, with a very small amount as **carbon**-13.

Here’s an example using the simplest atom, hydrogen. *Carbon*-14 is an unstable isotope of *carbon* that will eventually decay at a known rate to become *carbon*-12.

weather, speed); Integration using geometry; The fundamental theorem of *calculus*; u-substitution.

Click here for some practice problems on u-substitution (for more examples, look at your lecture notes). Office: PO103, Room 118 (PO103 is one of the portables just outside the Science Wing) Telephone: 416-208-2784 Email: leo.goldmakher at utoronto dot ca Office hours: Tuesday and Thursday -- pm, Tuesday --, and by appointment.

Set the midterm date for March 4th (in class); Practiced manipulating exponentials and logs; Discussed APR, nominal rates, effective rates, future value, and present value; Started a problem on *carbon* *dating* and half-life.

The ratio of *Carbon*-14 remaining indicates the times since the death of a living substance.

*Carbon*-14 only works for things between 3 and 40 thousand years old. *Carbon* *dating* is based on an isotope of *carbon*, *carbon* 14, that's unstable. We breathe in *carbon* dioxide, we eat *carbon*, we take in *carbon* and so our bodies continually renewing our supply of *carbon* 14.