Calculate the age of a plant sample that shows about one-eighth of the carbon 14 of a living sample. The half-life of carbon-14 is about 5760 a.

Help please...

Solve for k using k = 0.693/t1/2, then substitute k into the following:

ln(No/N) = kt
Use No = 8
N = 1
k from above.
t = unknown.

Is that

0.693/
t 1/2

0.693 over t one half ?

yes. k = 0.693/5760 = ? yr^-1

In the start of the equation .. for

In(No/N) I understand the No/N is the percentage that the sample is of carbon 14 compared to a living sample, but how do you get the In ? where does it come from ?

This is the integrated equation for a first order rate reaction. All of them are

ln(No/N) = kt
I can probably find a place on the web that derives the equation if you really want it. There isn't much to understand about it at this point except how to use it. The problem tells you that the radioactivity is 1/8 of the original; that's the 8/1. No is what you start with and N is what is there currently.

http://en.wikipedia.org/wiki/Rate_equation#First-order_reactions

To calculate the age of a plant sample using carbon-14 dating, you need to use the concept of half-life. The half-life of carbon-14 is approximately 5760 years, which means that after each half-life period, the amount of carbon-14 in a sample decreases by half.

In this problem, you are given that the plant sample shows about one-eighth (1/8) of the carbon-14 in a living sample.

To solve this, we can set up the following equation:

(1/8) = (1/2)^(n)

In this equation, 'n' represents the number of half-lives that have occurred.

To solve for 'n', we need to take the logarithm of both sides of the equation. Taking the logarithm base 2 (since we have a fraction with a denominator of 2), we get:

log2(1/8) = log2((1/2)^(n))

Simplifying further:

-3 = n * log2(1/2)

Using the property of logarithms that logb(b^x) = x, we can simplify this equation to:

-3 = n * (-1)

Now, solving for 'n':

n = (-3) / (-1) = 3

Therefore, 'n' is equal to 3, meaning that the plant sample has undergone 3 half-lives.

To calculate the age of the plant sample, we need to multiply the number of half-lives (n) by the half-life period of carbon-14 (5760 years):

Age of plant sample = n * half-life period

Age of plant sample = 3 * 5760 years

Age of plant sample = 17,280 years

So, the age of the plant sample is estimated to be approximately 17,280 years.