00:01
We are asked to figure out how long it takes carbon 14, specifically 2 .4 grams of it to be reduced to 1 .3 grams.
00:11
So let's start with the radioactive decay equation, which says a of t is equal to a sub 0 times e to the r times t.
00:19
Let's write a second equation.
00:21
We know that the half life of carbon 14 is 5 ,730 years.
00:25
So, one half times the initial amount should be equal to the initial amount times er times 5 ,730.
00:47
Now, a sub 0 is the same base, which means we can initially drop it.
00:54
We would have one half is equal to er 5 ,730.
01:05
Now, if we ln both sides, we would get ln of one half is equal to.
01:14
Now, the exponent is dropped down, so we would have r times 5 ,730.
01:22
Now, ln of e is equal to 1, so we don't need to write that...