SOLUTION: 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

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Question 327777: Use the formula N=Ie%5Ekt, 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 approximzte age of the artifact? (carbon-14 decays at the rate of 0.0125% annually.)

possible answers(5200 years, 3446 years, 1497 years, 2800 years.)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Use the formula N=Ie%5E%28kt%29, 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%5E%28kt%29=N
where:
N = .65
I = 1
k = -.000125, decay is negative
Find t
:
1%2Ae%5E%28-.000125t%29=+.65
Using nat logs
ln%28e%5E%28-.000125t%29%29=+ln%28.65%29
Find ln
-.000125t = -.43078
t = %28-.43078%29%2F%28-.000125%29
t = +3,446 yrs