SOLUTION: this word problem uses a formula that the book talked about very briefly and I did not understand it...N=Iekt,where n = number of items in terms of the initial population, I, at ti
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Question 314890: this word problem uses a formula that the book talked about very briefly and I did not understand it...N=Iekt,where n = number of items in terms of the initial population, I, at time t, and k is the growth constant equal to the % of growth per unit of time
an artifact is found 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)
please show work so I can understand this formula better and how to do the problem.
THANKS IN ADVANCE Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
Your given equation:
is the standard exponential growth/decay formula
where
N is the amount after time t
I is the initial amount
k is the growth/decay rate
t is time
.
If k is positive it is "growth" otherwise k is negative or "decay".
.
Given your problem:
an artifact is found 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)
.
Notice the problem doesn't give you the initial amount so assign it a variable:
Let x = initial amount
then
N is .65x
I is x
k is 0.0125% or 0.000125
t is what we need to find
.
Plug in what was given into:
Now, solve for t:
Start, by dividing both sides by x:
Next, take the natural log of both sides: years
.
Or, it is about 3446 years old.
