the activity of a sample of carbon has one-eighth of the initial activity. carbon-14 has a half-life of 5730 yr. how old is the sample in yr?

Answer 1

one eighth is three half-lives.

Now the hard way:

amount left=original amount(1/2)^t/thalflife

1/8=(1/2)^t/th

t/th=3

or even harder:

amountleft=original*e^-.693t/th

1/8=e^-.693 t/th

ln of each side

ln (1/8)=-.693 t/th
-2.0793=-.693 t/th

t/th= 3

Answer 2

the question ask how old is the sample in yr. so that mean t/th is 3 yrs.