How long has the tree been dead?

Drop the course since you can't just write down
p1=p0 2^-(t/tau), solve for t
Either you haven't studied or this stuff is way above your IQ.

In either case, drop the course.

The problems with carbon dating and similar techniques for dating are numerous. For one, it assumes a regular behavior in what is otherwise accepted as a random event. For two, different dating techniques produce drastically different, sometimes contradictory results. For three, like any science, it relies on probabilistic reasoning and statistics; never mind theory that cannot be verified. For four, it assumes that the concentration of certain isotopes found in nature at the time the fossil is dated is the same as it is today; and that.... for five, no special event occurred that introduced more or less than what is typical. Six, it it utterly unverifiable and utterly non-repeatable in laboratory conditions. In fact, some laboratory experiments have indeed suggested that some of the assumptions relied on are erroneous.