Carbon dating math problem

If feet of pipe can be represented by the following equation: Suppose that the pollutants must be reduced to 10% in order for the kerosene to be used for jet fuel.

How long does the pipe have to be to ensure that there is only 10% of the pollutants left in the kerosene?

This half life is a relatively small number, which means that carbon 14 dating is not particularly helpful for very recent deaths and deaths more than 50,000 years ago.

After 5,730 years, the amount of carbon 14 left in the body is half of the original amount.

So now we're solving for a variable and the exponent, whenever we see that, we need to just take the natural log.

We take a natural log because it's the base e, we could take the log, but then we'd be left with a log b, so we take the natural log, this is going to make our base to disappear.

At any particular time all living organisms have approximately the same ratio of carbon 12 to carbon 14 in their tissues.

In the case of radiocarbon dating, the half-life of carbon 14 is 5,730 years.It doesn't really matter that we don't know the exact amount, we're still trying to solve the same exact way.So now we have a exponential equation, except we have n zero on the same side which is a variable we don't know what it is so all we have to do is divide by that n zero, divide both sides it cancels way all together and we're just left with that 71% equals e to the small negative number t.The kerosene is purified by removing pollutants, using a clay filter.Suppose the clay is in a pipe and as the kerosene flows through the pipe, every foot of clay removes 20% of the pollutants, leaving 80%.The trick is that we don't know how much we started with, so we can't plug in a number, so we're still left with N sub 0, we're left with e to the -.00012t, because we don't know how much we started with, we also don't know how much we ended with, but we do know we have 71% of our original amount.So this is our entire amount, if I said we had half of that we would just multiply this by a half.They found a stick that had 71% of it's original carbon-14, so they know how much carbons should be in this stick say it's oak or whatever it maybe and there's lots of Math, so they know that some has decayed over time.Using carbon-14 dating, so basically exponential decay, and this particular rate, we're supposed to figure out how old the tomb is. So we know our decay formula to be N is equal to N zero, e to the rt and they told us that our rate is a very small negative number and we have 71% of the original amount and we're supposed to find the time, we're supposed to find t.So it's just a little bit of an introduction into carbon-14 dating.Basically it's exponential decay when you know the amount of a substance remaining, you can figure out how long it has been decaying.