Carbon sample of a saber tooth tiger decay

[graphicer89]

Homework Statement

A carbon sample taken from the bone of a saber tooth tiger emits 1 beta emission a minute. A carbon sample of the same size taken from a frest piece of bone emits 16 beta emissions a minute. How long ago did the saber tooth tiger live? How can i do this?

Homework Equations

Are there any equations for this?

The Attempt at a Solution

Well i don't even know where to start honestly...Please at least start me off the right path..

 

[cepheid]

Radioactive decay occurs exponentially. I imagine you must have some information about it in your notes or something, if you are being asked about it?

 

[graphicer89]

Radioactive decay occurs exponentially. I imagine you must have some information about it in your notes or something, if you are being asked about it?

Well honestly I thought so too but no I don't have anything

 

[ideasrule]

Well honestly I thought so too but no I don't have anything

Try reading up on half-life & radioactive decay in your textbook or on the Internet. After you've done that...

Radioactive decay is a truly random process; no scientist/sage/god/whatever can predict when a given atom will decay. That means that in one second, the number of atoms that decay is proportional only to the amount of radioactive material left. So the ancient tiger tooth in your question contains 1/16 the mass of C-14 in a still-living tiger's tooth. There's a reason that 16 is precisely 2^4...

 

[graphicer89]

Try reading up on half-life & radioactive decay in your textbook or on the Internet. After you've done that...

Radioactive decay is a truly random process; no scientist/sage/god/whatever can predict when a given atom will decay. That means that in one second, the number of atoms that decay is proportional only to the amount of radioactive material left. So the ancient tiger tooth in your question contains 1/16 the mass of C-14 in a still-living tiger's tooth. There's a reason that 16 is precisely 2^4...

Ok so right now i know that half life is 5730 years...and I am trying to figure out the 1/16 the saber tooth lived compared to the recent new one...So i think this is basically a math problem but i have no idea where to start...please help me out..i really want to learn but after reviewing what i was given as a guide..this is all i came up with...

 

[graphicer89]

What i got was that i multiply...16 x 5730 years...= 91,680 years ago...how does that sound?

 

[kuruman]

What i got was that i multiply...16 x 5730 years...= 91,680 years ago...how does that sound?

Not right. Consider the fresh piece of bone that emits 16 betas a minute.

In how many years will it emit 8 betas a minute? Hint: 8 is half of 16.
In how many years will it emit 4 betas a minute?
In how many years will it emit 2 betas a minute?
In how many years will it emit 1 beta a minute?

Note that when the tiger died, all its bones were "fresh."

 

[rl.bhat]

In one half life, the activity decreases to half.
In four half life, the activity decreases to 1/16.
So the age of the tooth is 4xhalf life of carbon.