_{0}e-

^{kt}

_{0}is the starting amount and k is the decay constant.

_{0}= e

^{-kt}= e

^{-[(0.00012)*(4000)]}= e

^{-0.48}= 0.62

_{0}).

A team of archaeologists recovered wooden artifacts believed to be 4000 years old. How much carbon-14 has been lost from the wood?

the decay rate for carbon -14 is 0.00012

I can't figure out how to put this in A formula.... Any help is appreciated!

Tutors, sign in to answer this question.

Dear Erica,

In general

A = A_{0}e-^{kt}

where A is the amount remaining after t years, A_{0} is the starting amount and k is the decay constant.

Let us rewrite this as

A/A_{0} = e^{-kt} = e^{-[(0.00012)*(4000)]} = e^{-0.48} = 0.62

I think all we can say with certainty is that, during those 4000 years, the amount of C-14 decreased to 62% of its original value, or it lost 38% of its original value (A_{0}).

N(t)=N(0)e^{-kt}, where k is the decay rate. I assume k=-0.00012 is measured in year^{-1}, so that t is in years (in fact, it is the case, I believe, since half-life time is 5730 years for C^{14}).

Then,

N(4000)/N(0)=e^{-0.00012*4000}=e^{-0.48}≈0.62

So the amount of carbon-14 left at the present moment is 0.62 or 62% of its original quantity. Therefore, 38% has been lost due to decay.

Answer: 38%

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.