Solve Logarithm: Find n if P=76%, k=-5668, P=2^{-kn}

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Homework Statement


It was found that the percentage of the carbon-14,P, contained in the bones of an animal n years after it has died is given by P = 2[tex]^{-kn}[/tex] , where k is a positive constant. The percentage of carbon-14 contained in the bones after the animal has been dead for 5668 years was 50% . How long, to the nearest year, was the animal dead if the percentage of the carbon-14 found in the bones was 76%?

I tried however my K is negative.


Homework Equations





The Attempt at a Solution

 
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You tried? Good! Now, what did you try? Show exactly how you got K negative and we may be able to help you. (Perhaps you used P= 50 instead of 0.50?)
 
HallsofIvy said:
You tried? Good! Now, what did you try? Show exactly how you got K negative and we may be able to help you. (Perhaps you used P= 50 instead of 0.50?)

why is it 0.5 and not 50? i thought they were asking for the percentage and not the fraction?

The k i got is log , base 2, 50 over -5668
 
You use 0.5 because 50%=50/100=5/10=1/2=2-1
[tex]2^{5668k}=2^{-1}[/tex]
Now you need to find k and then substitute in 2-kn=76/100 and find n
 
icystrike said:
why is it 0.5 and not 50? i thought they were asking for the percentage and not the fraction?

The k i got is log , base 2, 50 over -5668
Where did you get the idea that they were asking for a percentage? The problem specifically said " How long, to the nearest year". "How long" is NOT a percentage!