# Carbon dating using exponential growth internet interracial dating

The method of carbon dating makes use of the fact that all living organisms contain two isotopes of carbon, carbon-12, denoted 12C (a stable isotope), and carbon-14, denoted 14C (a radioactive isotope).

The ratio of the amount of 14C to the amount of 12C is essentially constant (approximately 1/10,000).

Archaeologists use the exponential, radioactive decay of carbon 14 to estimate the death dates of organic material.

The stable form of carbon is carbon 12 and the radioactive isotope carbon 14 decays over time into nitrogen 14 and other particles.

When an organism dies, the amount of 12C present remains unchanged, but the 14C decays at a rate proportional to the amount present with a half-life of approximately 5700 years.

This change in the amount of 14C relative to the amount of 12C makes it possible to estimate the time at which the organism lived.

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.In the case of carbon-14, I'll tell you what percentage of my original carbon-14 has not decayed into nitrogen, as yet, nitrogen-14.And that's useful, but what if I care about how much carbon I have after 1/2 a year, or after 1/2 a half life, or after three billion years, or after 10 minutes? A general function, as a function of time, that tells me the number, or the amount, of my decaying substance I have.How long does the pipe have to be to ensure that there is only 10% of the pollutants left in the kerosene?This means that we need a pipe that is 10.3 feet long in order for the pollutants to be reduced to 10% of their starting amount.

For example, where time equals zero, we have 100% of our substance.