Question 577777
The half-life of 234U, uranium-234, is 2.52 multiplied by 105 yr.
 If 97.7% of the uranium in the original sample is present,
 what length of time (to the nearest thousand years) has elapsed? 
:
The radioactive decay formula: A = Ao*2^(-t/h) where:
A = resulting amt after t time
Ao = initial amt (t=0)
h = half-life of substance
t = time in yrs
:
I think you mean the half-life of uranium-234 is: 2.52(10^5) yrs
Let Ao = 1,
A = .977
 find t
:
1*2^[-t/2.52(10^5)] = .977
using logs
{{{log(2^(-t/2.52(10^5))) = Log(.977)}}}
log equiv of exponents
{{{-t/(2.52(10^5))}}}*log(2) = log(.977)
:
{{{-t/(2.52(10^5))}}} = {{{log(.977)/log(2)}}}
using a calc 
{{{-t/(2.52(10^5))}}} = -.033569
t = {{{-.033569*-2.52(10^5)}}}
:
t = +8459.5 ~ 8000 yrs to the nearest thousand