The two solutions provided differ slightly in their approach in this regard.

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

Libby invented carbon dating for which he received the Nobel Prize in chemistry in 1960.

The task requires the student to use logarithms to solve an exponential equation in the realistic context of carbon dating, important in archaeology and geology, among other places.

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 standards do not prescribe that students use or know with log identities, which form the basis for the "take the logarithm of both sides" approach.

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

C) dating usually want to know about the radiometric[1] dating methods that are claimed to give millions and billions of yearsâ€”carbon dating can only give thousands of years.

People wonder how millions of years could be squeezed into the biblical account of history. Christians, by definition, take the statements of Jesus Christ seriously.

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

The amount of Carbon 14 contained in a preserved plant is modeled by the equation $$ f(t) = 10e^{-ct}.

$$ 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).

So when $t = 0$ the plant contains 10 micrograms of Carbon 14.

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