anonymous
  • anonymous
A hiker in Africa discovers a skull that contains 63% of its original amount of C-14. N=Noe^-kt No=initial amount of C-14(at time t=0) N=amount of C-14 at time t t=time, in years k=0.0001
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
Ok so we have: \[ N(t)=N_o e^{-kt}\]
anonymous
  • anonymous
We are told that their is 63% of C14 remaining in the material hence: \[ \frac{N(t)}{N_o}= 63\% =0.63= e^{-kt}\]
anonymous
  • anonymous
yes but it says find the age of the skull to the nearest year.

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
Taking the ln of both sides: \[\ln(0.63)= -(0.0001 yr^{-1})t\]
anonymous
  • anonymous
Divide and you have you answer
anonymous
  • anonymous
divide 0.63 / -0.0001?
anonymous
  • anonymous
Please note it isnt 0.63 but ln(0.63)
anonymous
  • anonymous
And then it is a yes
anonymous
  • anonymous
Btw, in case your worried about the minus sign... the fact that the argument of the logarithm is <1 means its result will be <0.... so the minus signs cancel and it will yield a positive value for t
anonymous
  • anonymous
i got -6300
anonymous
  • anonymous
natrual log of 0.63 divided by -10^-4
anonymous
  • anonymous
Please note that the CRUCIAL step in this problem was taking the log of both sides. Without that step you cannot reduce the exponential factor.
anonymous
  • anonymous
your confusing me
anonymous
  • anonymous
What do you find confusing?
anonymous
  • anonymous
Please, I cant help if I dont know where your getting confused.
anonymous
  • anonymous
Go through the process I did at the top and let me know which step you are uneasy about and I will give a more detailed explanation.
alekos
  • alekos
show him the steps in detail
anonymous
  • anonymous
I was under the impression I did alekos but I will go through it again.
anonymous
  • anonymous
Ok so we given in the problem that the amount of C14 we find in the skull is 63%
anonymous
  • anonymous
This means that of the original amount: \[N_0=100\% (some \ amount \ of \ nuclei)=(some \ amount \ of \ nuclei) \] It decays according to the law \[N(t)=N_0 e^{-kt}\] Where the N's correspond to the number of nuclei of the material in quesion remaining (N(t)) or the original amount (N_0) So that at time T, we have: \[N(T)=63\% (some \ amount \ of \ nuclei)=(some \ amount \ of \ nuclei) e^{-kT}\] Now whatever the total amount of nucleai there are in the sample is irrelevant because I can just divide both sides by that amount leaving just the percent remaining.
anonymous
  • anonymous
This results in the equation I gave above: \[63\% = 0.63=e^{-kT}\]
anonymous
  • anonymous
Now just like when we have an equation of the form: \[2=x^2\] Which we solve by applying the inverse function of squared (i.e. the square root) to both sides (ignoring the +/- that comes in for simplicity): \[\sqrt{2}=\sqrt{x^2}=x\] When we have an exponential equation of the form: \[2=e^x\] We apply the inverse function to the exponential function (aka the natural logarithm) to both sides in order to simplfy and solve: \[ \ln(2)=\ln(e^x)=x\]
anonymous
  • anonymous
Note that an exponential function can NEVER be negative (unless I explicitly multiply it by a -1), which means when I do this inverse function business applying the logarithm, I dont have to worry about a +/- like you do when you apply a square root. So don't let that trouble you.
anonymous
  • anonymous
So performing this step (taking the natural log of both sides of the equation) yields: \[\ln{0.63}=\ln{e^{-kT}}=-kT=-(10^{-4}yr^{-1})T\] Then solve for T, by dividing both sides by k: \[T=\frac{\ln{0.63}}{-(10^{-4}yr^{-1})}\]
anonymous
  • anonymous
Please calculate this value and express it with the appropriate units here I and I will check your answer.
anonymous
  • anonymous
@ix.ty are you still here?
anonymous
  • anonymous
im on a diffrent question now
anonymous
  • anonymous
A country's population in 1992 was 222 million. In 2001 it was 224 million. Estimate the population in 2004 using the exponential growth formula. Round your answer to the nearest million. P = Aekt
anonymous
  • anonymous
So what did you get for the last one?
anonymous
  • anonymous
i got it wrong that was my last question but i passed the test
anonymous
  • anonymous
Oh so before I even try to start what looks to be a HARDER question on the same material it bears going over the last problem to iron out what confused you. Please tell me what you found confusing.
anonymous
  • anonymous
No judgement, I fancy myself like a bit of an auto-mechanic.... I need to know where the problem is in order to try and fix it.
alekos
  • alekos
dont bother plasma, seems like you're wasting you're time
anonymous
  • anonymous
Perhaps, but I am stubborn and banging my head against the wall might be a bit of a pastime for me.... But either way I am willing to help @ix.ty but I will only stick around for maybe 10-20 minutes (Ill check back at this tab) then I will move on

Looking for something else?

Not the answer you are looking for? Search for more explanations.