A fossil found in an archaeological dig was found to contain 20% of the original amount of 14C. I do not get the $-0.693$ value, but perhaps my answer will help anyway.If we assume Carbon-14 decays continuously, then $$ C(t) = C_0e^, $$ where $C_0$ is the initial size of the sample. Since it takes 5,700 years for a sample to decay to half its size, we know $$ \frac C_0 = C_0e^, $$ which means $$ \frac = e^, $$ so the value of $C_0$ is irrelevant. This is why it is such a big concern when a nuclear submarine sinks... (By the way, you are mostly Carbon-12, which is not radioactive.Eventually, the salt water will eat through the steel and release the Plutonium (which, as you know, is quite lethal.) They usually talk about either trying to raise the sub or encase it in concrete where it rests. That's why we are called "Carbon-based life forms." Man, I've really watched too much Star Trek.)Scientists use Carbon-14 to make a guess at how old some things are -- things that used to be alive like people, animals, wood and natural cloths. Anyway, they make an estimate of how much Carbon-14 would have been in the thing when it died...Why isn't the skin of aircraft and cars similarly dimpled? Runners have long debated the difference between training on a treadmill and training on solid ground.
So given that the half-life of carbon-14 is 5730 years, consider a sample of fossilized wood that, when alive would have contained 24 g of carbon-14.
$$ Time in this equation is measured in years from the moment when the plant dies ($t = 0$) and the amount of Carbon 14 remaining in the preserved plant is measured in micrograms (a microgram is one millionth of a gram).
So when $t = 0$ the plant contains 10 micrograms of Carbon 14.
I understand it's less common in men than women – presumably this is down to footwear choices?
The cream product I use to cure it works very well, but its active ingredient appears to be urea.