Carbon dating has given archeologists a more accurate method by which they can determine the age of ancient artifacts.

Natasha Glydon Exponential decay is a particular form of a very rapid decrease in some quantity.

One specific example of exponential decay is purified kerosene, used for jet fuel.

A fossil found in an archaeological dig was found to contain 20% of the original amount of 14C. I do not get the $-0.693$ value, but perhaps my answer will help anyway.

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.

If feet of pipe can be represented by the following equation: Suppose that the pollutants must be reduced to 10% in order for the kerosene to be used for jet fuel.

How long does the pipe have to be to ensure that there is only 10% of the pollutants left in the kerosene?

The amount of Carbon 14 contained in a preserved plant is modeled by the equation $$f(t) = 10e^.$$ Time in this equation is measured in years from the moment when the plant dies ($t = 0$) and the amount of Carbon 14 remaining in the preserved plant is measured in micrograms (a microgram is one millionth of a gram).

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

Carbon is naturally in all living organisms and is replenished in the tissues by eating other organisms or by breathing air that contains carbon.

Students should be guided to recognize the use of the logarithm when the exponential function has the given base of $e$, as in this problem.

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