Need help with logarithm/exponential functione problems(2)

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April 8th 2010, 08:49 PM
farhadfarzadsucks

I'm in pre-calculus and I'm completely clueless with these 2 problems.
1) The radioactive isotope of carbon-14c has a half life of 5730 years.
A) What is the decay constant of carbon-14c
B) If we start with a sample of 1000 carbon14 nuclei, how many will be left in 22,290 years time.

2) A Piece of charcoal of mass 25g is found in the ruins of an ancient city. The sample shows a carbon-14 activity or R(t)= 4.167 decays/second.
A) Convert the decay constant of carbon-14c from (1)(a) in terms of seconds instead of years.
B) Find the number f remaining atoms of N(t) using the constant you found in (a)
C) Suppose that the initial number of carbon-14c nuclei before decay is 1.63x10^12. What was the initial rate of decay ( or R initial)
D) How long has the tree that this charcoal came from been dead?

Okay so I'm given these equations

N(t)=Ninitial*e^-ct

R(t)=Rinitial*e^-ct

http://i40.tinypic.com/124hfdl.jpg
April 8th 2010, 09:14 PM
xsavethesporksx

Quote:

Originally Posted by farhadfarzadsucks

I'm in pre-calculus and I'm completely clueless with these 2 problems.
1) The radioactive isotope of carbon-14c has a half life of 5730 years.
A) What is the decay constant of carbon-14c
B) If we start with a sample of 1000 carbon14 nuclei, how many will be left in 22,290 years time.

2) A Peice of charcoal of mass 25g is found in the ruins of an ancient city. The sample shows a carbon-14 activity or R(t)= 4.167 decays/second.
A) Convert the decay constant of carbon-14c from (1)(a) in terms of seconds instead of years.
B) Find the number f remaining atoms of N(t) using the constant you found in (a)
C) Suppose that the initial number of carbon-14c nuclei before decay is 1.63x10^12. What was the initial rate of decay ( or R initial)
D) How long has the tree that this charcoal came from been dead?

Okay so I'm given these equations

N(t)=Ninitial*e^-ct

R(t)=Rinitial*e^-ct

So the equation for part 1, Since you know that your initial amount is 1/2 at time t=5730, you can assume values for your initial and final values
i'll use 10 and 20 as an example

$1/2N(t)=Ne^(-ct)<br /> (1/2)20=20e^(-c*5730)$

Then use properties of logs to solve for c and this will be the decay rate

Part 2, use that decay rate to determine the amount left after t=22,290
April 8th 2010, 09:45 PM
farhadfarzadsucks

Quote:

Originally Posted by xsavethesporksx

So the equation for part 1, Since you know that your initial amount is 1/2 at time t=5730, you can assume values for your initial and final values
i'll use 10 and 20 as an example

$1/2N(t)=Ne^(-ct)<br /> (1/2)20=20e^(-c*5730)$

Then use properties of logs to solve for c and this will be the decay rate

Part 2, use that decay rate to determine the amount left after t=22,290

Uhm, I haven't learned that method or not used to doing that.

Or do I just plug in the numbers?