Question

help me PWEASEEEEE
In order to understand the prehistory of the Hawaiian island of Lana'i better, anthropologists Maria Sweeney, Melinda Allen, and Boyd Dixon used radiocarbon dating on charcoal found in an ancient dwelling site, the Kaunolu Village National Historic Landmark, the largest archeological complex on the island. In one of their samples, they found that approximately 94% of the original carbon 14 remained. Using the fact that Carbon 14 decays by 1.202% every 100 years, determine the approximate age of the this sample .

Answer 1

1200 years

Answer 2

... how do u know i dont need the answer i need to know how...

Answer 3

The voice in my head told me.

Answer 4

you need a formula for this

Answer 5

im guessing so ... i think it involves LOGs

Answer 6

decays be 1.202% every 100 years means every 100 years you would multiply by 100%-1.202%= .98798

Answer 7

so you can use
\[A=A_0\times (.98798)^{\frac{t}{100}}\]

Answer 8

what is the 0 after A signify?

Answer 9

don't worry about the \(A\) and the \(A_0\)

Answer 10

A is your amount in \(t\) years, it is a function \(A(t)\) and \(A_0\) is what you start with

Answer 11

oh ok so logarithms aren't used in this problem?

Answer 12

but you don't need to worry about that, because whatever you start with you know you have 94% left, so solve
\[.94=(.98798)^{\frac{t}{100}}\] for \(t\) and yes, you need logs

Answer 13

oh ok give me a sec i wanna try this on paper

Answer 14

ok should take two steps only

Answer 15

ok im lost i got log 94/100/ log(1-.01202)

Answer 16

did you start with
\[
.94=(.98798)^{\frac{t}{100}}\]?

Answer 17

oh looks sort of good but you have too many fraction bars

Answer 18

the log94/100 is over log(1-.1202)

Answer 19

\[\frac{t}{100}=\frac{\ln(.94)}{\ln(.98798)}\]
\[t=100\times \frac{\ln(.94)}{\ln(.98798)}\]

Answer 20

wait u lost me im supposed to do this on excel and i have no clue how that applies

Answer 21

me neither
i used this
\[A=b^x\iff x=\frac{\ln(A)}{\ln(b)}\]

Answer 22

hmmm ok im gonna try to figure this out by myself give me a couple

Answer 23

was the answer 5.12

Answer 24

off by some decimal places
http://www.wolframalpha.com/input/?i=100ln%28.94%29%2Fln%28.98798%29

Answer 25

it is 5.12 before you multiply by 100

Answer 26

because the exponent is not \(t\) it is \(\frac{t}{100}\) so you have to multiply by 100 to get \(t\) after taking the log