Half-Life Problem... I'm stumped

[geekygal]

Hi i am having a bit of a problem starting this half life problem. Please just help me get started and basically what im supposed to do and I can do the integration, etc

The 1/2 life of C^14 is 5568 years. How long has some previously living matter been dead if the remains have only 20% of the original amount when the plant was alive?

Thank you in advance

 

[wjm11]

i am having a bit of a problem starting this half life problem. Please just help me get started and basically what im supposed to do and I can do the integration, etc

The 1/2 life of C^14 is 5568 years. How long has some previously living matter been dead if the remains have only 20% of the original amount when the plant was alive?

No integration is required for this problem.

Let’s start by looking at a general form of an exponential function and figuring out what the various parts mean:

y = a(b)^x

The a and b are constants that depend on the particular problem. The x and y are the variables, and x is the exponent of b; if we put in a value for x, we can calculate a value for y (assuming we already know what the constants, a and b, are).

In “half-life” problems, we’re using the above equation. The “a” constant is our starting amount. “b” is set to ½.

The “x” is the “amount of time we’re interested in” divided by the half-life period. Dividing the elapsed time by the half-life tells us the number of half-lives that have gone by.

The “y” is the final amount after a given time period has elapsed:

Final amount = (initial amount)(1/2)^[(elapsed time)/(half-life)]

In your specific problem, we’re given the all the information on the initial amount (100% = 1.00), half-life, and the final amount (20% = .2). Your job is to find the elapsed time.

Can you handle it from here?

 

[geekygal]

Yes, thank you That really helped me to understand the problem =)