# Carbon dating using exponential growth

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.   Alright, so, like always, pause the video and see if you can come up with this function, M, that is going to be a function of t, the years since the initial measurement. What I like to do is, I always like to start off with a little bit of a table to get a sense of things. However many half-lifes we have, we're gonna multiply, we're gonna raise 1/2 to that power and then we multiply it times our initial mass.

\$\$ 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.

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

- [Voiceover] We're told carbon-14 is an element which loses exactly half of its mass every 5730 years.

Alright, so, like always, pause the video and see if you can come up with this function, M, that is going to be a function of t, the years since the initial measurement. What I like to do is, I always like to start off with a little bit of a table to get a sense of things. However many half-lifes we have, we're gonna multiply, we're gonna raise 1/2 to that power and then we multiply it times our initial mass.\$\$ 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.Above is a graph that illustrates the relationship between how much Carbon 14 is left in a sample and how old it is.- [Voiceover] We're told carbon-14 is an element which loses exactly half of its mass every 5730 years.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.