SOLUTION: The mass of a radioactive element at time x is given by the equation below, where c is the original mass and h is the half-life of the element. How old is a mummy that has lost 55%

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Question 589026: The mass of a radioactive element at time x is given by the equation below, where c is the original mass and h is the half-life of the element. How old is a mummy that has lost 55% of its carbon-14 (its half-life is 5730 years)? (Round your answer to the nearest year.)
Formula given M(x)= c(.5^x/h)
Please help me solve this problem please.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The mass of a radioactive element at time x is given by the equation below,
where
c is the original mass and
h is the half-life of the element.
:
How old is a mummy that has lost 55% of its carbon-14 (its half-life is 5730 years)? (Round your answer to the nearest year.)
>
Formula given M(x)= c(.5^x/h)
:
Let the original amt of carbon = 1
then
1-.55 = .45 remains
Find x, years of decay
:
1*.5^(x/5730) = .45
:
Use natural logs
ln*(.5^(x/5730)) = ln(.45)
;
log equiv of exponents
x%2F5730ln(.5) = ln(.45}
x%2F5730 = ln%28.45%29%2Fln%28.5%29
:
use your calc
x%2F5730 = 1.152
x = 1.152*5730
x = 6601 yrs
:
:
Check this on your calc; enter: .5^(6601/5730) ~ .45 which 45% remaining