Question

Diff. Equations
Suppose that a particular carbon isotope which is found in living trees has a half-life of 5700 years. Scientists have discovered that the charcoal from a tree burned in a volcanic eruption contains 36 percent of the isotope level that is normally found in living trees.

How many years ago did the volcanic eruption occur?

Answer 1

@Directrix @AccessDenied Could you please help here?

Answer 2

Ok - are you familiar with the equation A(t) = A(o) e^-kt?

Answer 3

@zhang950609

Answer 4

A(t) is the amount of the material after a certain time, t has elapsed.
A(o) is the initial amount of the material
e is the natural log, in number 2.71828
k is the constant which can be derived from the half life. And t is the time...
in 2/half life=k, so we can use the half life to solve for k.

Answer 5

@zhang950609 can you please write whatever you want to write in here!

Answer 6

make sense, but can you write down more specific details about it? like using the number i mentioned. thanks :)

Answer 7

Yes - if we know that 36% remains that means that y(t)/y(l) is 36% right? So we convert to decimal format which is .36

Answer 8

We can divide each side so we have y(t)/y(o)
= e^-kt and then we know that y(t)/y(o) is just the 36% which is .36

Answer 9

yes. i used to write 0.36yo=y0exp(-(5700/ln(2))t) for solving y, however, the answer i got was wrong. i dk why

Answer 10

in2/half life right?
We need to divide in2/half life and multiply that by the time, 5700

Answer 11

yes, it is half time. what u mean time 5700? can you type down the equation u r going to use?

Answer 12

yes - I'm using the same equation A(t) = A(o) e^-kt.
5700 is the time, half life sorry.

Answer 13

in .36= .693/5700 years *t

Answer 14

my setup looks like that I take the ln of each side to get rid of e^

Answer 15

Does it make sense? [:

Answer 16

yes it does! what is ur final answer? btw, can u write it like "1/5", not "0.2" thanks

Answer 17

i got [ln(36/100)ln(2)]/5700, but the system said i am wrong :(

Answer 18

Hmm do you mean 36/100 another way of writing percents instead of decimal form. I can check your answer, what are you getting?