Question

MEDALS
A fossilized leaf contains 15% of its normal amount of carbon 14. How old is the fossil (to the nearest year)? Use 5600 years as the half-life of carbon 14. Solve the problem.

what would be the number??

Answer 1

first write 15% as \(.15\) because math uses numbers, not percents
then to right to the equation
\[\large \left(\frac{1}{2}\right)^{\frac{t}{5600}}=.15\] solve for \(t\) in one step (plus a calculator)

Answer 2

you know how to solve it ?
if not, let me know
it actually takes two steps, i lied

Answer 3

CAnt figure it out on my calc?

Answer 4

yea

Answer 5

what are you trying to enter?

Answer 6

the whole equation

Answer 7

lol no you cannot enter the whole equation, you have to solve for \(t\)

Answer 8

lets go slow
first of all, is it clear where i got \[\large \left(\frac{1}{2}\right)^{\frac{t}{5600}}=.15\] from ?

Answer 9

im 23 doing 12th grade math ... help me out lol

Answer 10

online thing

Answer 11

ok..

Answer 12

ok
lets first of all get the answer, and then see where the equation came from

Answer 13

wud it b 15299

Answer 14

i hvae 3 minutes to put my answer in

Answer 15

the way you solve
\[b^x=A\] for \(x\) is by the "change of base" formula
\[b^x=A\iff x=\frac{\ln(A)}{\ln(b)}\]
in this example \(x=\frac{t}{5600}, b=\frac{1}{2}=.5, A=.15\) and so
\[\large \left(\frac{1}{2}\right)^{\frac{t}{5600}}=.15\]
\[\large \iff \frac{t}{5600}=\frac{\ln(.15)}{\ln(.5)}\]making
\[t=\frac{5600\ln(.15)}{\ln(.5)}\]

Answer 16

i get \(15327\)

Answer 17

http://www.wolframalpha.com/input/?i=5600ln%28.15%29%2Fln%28.5%29

Answer 18

not correct not one of my answers...

Answer 19

pick the one closest then

Answer 20

well that means the problem wasnt done correctly but ok

Answer 21

no actually i did it two different ways and arrived at the same answer
it means your answers are not correct, or someone did it not carefully enough

Answer 22

what is the answer closest to \(15327\) ?

Answer 23

15299 and 15327 are only 28 years apart, which is not much in the scale of 15 thousand years
i bet the grad student who wrote this problem rounded somewhere