If possible, the ink should be tested, since a recent forgery would use recently-made ink.

Carbon 14 is a common form of carbon which decays over time.

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

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.

Note that the purpose of this task is algebraic in nature -- closely related tasks exist which approach similar problems from numerical or graphical stances.

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).

(Whatever you're being treated for is the greater danger.) The half-life is just long enough for the doctors to have time to take their pictures.

The dose I was given is -younger copy of an earlier document (in which case it is odd that there are no references to it in other documents, since only famous works tended to be copied), or, which is more likely, this is a recent forgery written on a not-quite-old-enough ancient parchment.

The kerosene is purified by removing pollutants, using a clay filter.

Suppose the clay is in a pipe and as the kerosene flows through the pipe, every foot of clay removes 20% of the pollutants, leaving 80%.

The halflife of carbon 14 is 5730 ± 30 years, and the method of dating lies in trying to determine how much carbon 14 (the radioactive isotope of carbon) is present in the artifact and comparing it to levels currently present in the atmosphere.

Above is a graph that illustrates the relationship between how much Carbon 14 is left in a sample and how old it is.

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.