Carbon14
- Author:
- Alec Contreras
Carbon 14 Explanation
The reason this graph is able to function was because we knew that Carbon-14 decays with a half life over time and since the amount of time is very long we are able to use this function in order to approximate the amount of time that it takes for Carbon 14 to continue to decline.
First, to show the amount of time elapsed we take the components given: amount of atoms the proportion of it on planet frisbee (10%) and the fact that carbon had a half-life of 6,000 years. Now since we want the time elapsed , we take ten percent of the amount of atoms multiplied by the exponent of (1/2)^(x/6000).
After setting up this equation it should yield us a declining function and the equation should look like f(x)=1000(1/2)^(x/6000).
In order to figure out the exact time you could use a y-value and refer the inverse of the exponents to isolate x. For instance in this case I choose y or f(x) to equal 250 atoms to set up an equation: 250=1000(1/2)^(x/6000). I then reduced the like terms by moving 1000 to the other side leaving the exponent of (1/2)^(x/6000) by itself and yielding (1/4) on the other side. By taking the log2 of both bases I was able to bring down (x/6000)*(-1)=(-2). Eventually you will get x to equal 12,000 years. Point A allows us to see the exact time given the amount of atoms. In the end the relationship should yield a slower decrease in the rate of atoms inside carbon.