$$ 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.

what range of C^14 to C^12 ratio would the scientist expect to find in the animal remains?

The dose I was given is -younger copy of an earlier document (in which case it is odd that there are no references to it in other documents, since only famous works tended to be copied), or, which is more likely, this is a recent forgery written on a not-quite-old-enough ancient parchment.In other words, this function takes in a number of years, t, as its input value and gives back an output value of the percentage of carbon-14 remaining.So, if you were asked to find out carbon's half-life value (the time it takes to decrease to half of its original size), you'd solve for t number of years when in any remains will have broken down.So, objects older than that do not contain enough of the isotope to be dated.Conversely, the method doesn't work on objects that are too young. A small amount of that carbon is in the form of a radioactive isotope called in the remains of an organism or artifact, plug that value into a generalized equation, and calculate the age of those remains.

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