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) 
:
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/5730}}}ln(.5) = ln(.45}
{{{x/5730}}} = {{{ln(.45)/ln(.5)}}}
:
use your calc
{{{x/5730}}} = 1.152
x = 1.152*5730
x = 6601 yrs
:
:
Check this on your calc; enter: .5^(6601/5730) ~ .45 which 45% remaining