PV Gap

Daryl Said:

Carbon-14 Dating Questions?

We Answered:

1)
The decay formula is N(t) = N(0)e^kt where:
N(t) = amount of carbon 14 remaining after t years
N(0) = initial amount of carbon 14
k = decay constant
t = time in years

Unfortunately problem 1 has two unkowns; k and t.
However, the half-life of carbon 14 is known to be approximately 5730 years. Since we know the time and the amounts, we can calculate the constant k.
N(5730) = [N(0)e^(k*5730)]
Since after 5730 years, 1/2 will remain, then N(t) = N(0)/2.
N(0)/2 = N(0)e^(k*5730)
cancel out the N(0)'s on both side and replace with 1's.
1/2 = 1*e^(k*5730)
ln(1/2) = ln[e^(k*5730)]
-0.693147181 = k*5730
k = -0.000120968 (Do not round off since we will be using this in calculations and want the greatest accuracy. Only round off the final answers.)

Now that we know k, we can calculate the carbon 14 decimal amount remaining after 5300 years. So N(t) = N(5300).
N(t) = N(0)e^kt
N(5300) = N(0)e^kt
since we are dealing with percentages, we know that 100% is the original amount, and that is decimal 1.0. Therefore, N(0) = 1.0.
N(5300) = (1.0) * e^(-0.000120968 * 5300)
N(5300) = e^(-0.000120968 * 5300)
N(5300) = e^(-0.6411309)
N(5300) = e^(-0.6411309)
N(5300) = 0.526696446 = 52.67% remaining

2)
N(t) = N(0)e^kt
Since 5.5% = 0.055 in decimal, then N(t) = (0.055)N(0).
(0.055)N(0) = N(0)e^(-0.000120968 * t)
cancel out the N(0) on both sides and replace with 1's
(0.055) * 1 = 1 * e^(-0.000120968 * t)
0.055 = e^(-0.000120968 * t)
take natural log of both sides
ln(0.055) = ln(e^(-0.000120968 * t))
-2.900422094 = -0.000120968 * t
t = 23976.75279 = 23,977 years ago

3)
Since we know that 8% of the carbon has been lost, then 92% remains (100 - 8 = 92). Therefore, N(t) = (0.92)N(0).
N(t) = N(0)e^kt
(0.92)N(0) = N(0)e^(-0.000120968 * t)
cancel the N(0) on both sides and replace with 1's
(0.92) * 1 = 1 * e^(-0.000120968 * t)
(0.92) = e^(-0.000120968 * t)
take natural log of both sides
ln(0.92) = ln(e^(-0.000120968 * t))
-0.083381609 = -0.000120968 * t
t = 689.2859592 = 689 years ago

Carlos Said:

Fundamentalist Christians - at what point do you decide to stop believing in science?

We Answered:

Because otherwise they would have to admit that they had wasted their lives believing in bullshit. I mean, anybody who actually believes in Answers in Genesis, or tries to prove that science and religion coexist through bible quotes must be brain-dead.

Tom Said:

what was this cartoon called?

We Answered:

The Young Sentinels, Look up The Young Sentinels on Wikipedia's cartoon sites, for more information.

Julio Said:

How can I get to know Jesus more?

We Answered:

I'm not going to blow smoke out my ***, but I've been researching this Jesus of Nazereth person for about five years, and its led me to the conclusion that he may have never even existed to begin with. But I can't prove that.

Charlie Said:

If knowledge is power, would'nt claiming to know how man and the world was created be claiming to be God.?

We Answered:

-We'd need to have evidence that god even exists to have knowledge that anything at all came from god
-We still wouldn't know everything, even assuming god existed.
-You seem to not understand how evidence works and what objective and subjective things are. Up is subjective, for example.

Beatrice Said:

DBZ's most powerful earthlings vs. Akatsuki?

We Answered:

First of all anime can be changed on this whim they are in completely different universes the creators could make them super powerful in one week it's not real.And every member of earth special forces could beat them all at the same time by themselves considering Vegeta with a power level of 21000 could destroy the planet with one attack.Someone that can only destroy a village and it shortens their lifespan stands no chance naruto characters couldn't even handle one piece characters if nothing is changed.