Question 519070
I think you mean
The half-life of 234U, uranium-234, is 2.52(10^5) yrs.
:
 If 98.2% of the uranium in the original sample is present, what length of time (to the nearest thousand years) has elapsed?
:
The half-life formula: A = Ao*2(-t/h)
where:
A = resulting amt after t yrs
Ao = initial amt
h = half-life of substance
t = time of decay
:
Let initial amt; Ao = 100
A = 98.2, resulting amt
h = 2.52(10^5) yrs
find t
:
100*2^(-t/(2.52(10^5)) = 98.2
:
2^{{{-t/2.52(10^5)}}} = {{{98.2/100}}}
:
2^{{{-t/2.52(10^5)}}} = .982
:
{{{-t/2.52(10^5)}}}*ln(2) = ln(.982)
:
{{{-t/2.52(10^5)}}} = {{{ln(.982)/ln(2)}}}
:
{{{-t/2.52(10^5)}}} = -.0262
:
{{{t = -.0262*-2.52(10^5)}}}
t = 6,603.68 yrs