Question 327777
Use the formula {{{N=Ie^(kt)}}}, where N is the number of items in terms of the initial population 
I, at time t, and k is the growth constant equal to the percent of growth per unit of time. 
:
An artifact is discovered at a certain site.
 If it has 65% of the carbon-14 it originally contained, what is the 
approximate age of the artifact?
 (carbon-14 decays at the rate of 0.0125% annually.)
:
{{{Ie^(kt)=N}}}
where:
N = .65
I = 1
k = -.000125, decay is negative 
Find t
:
{{{1*e^(-.000125t)= .65}}}
Using nat logs
{{{ln(e^(-.000125t))= ln(.65)}}}
Find ln
-.000125t = -.43078
t = {{{(-.43078)/(-.000125)}}}
t = +3,446 yrs