An examination of the tissue sample revealed that 46% of the carbon-14 present in his body @ the time of his death had decayed. The half-life of carbon-14 is approximately 5728 years. How long ago did this man die?

You can make use of the formula:

N = N_o \(\frac12\)^{\frac{t}{h}}

Where N is the initial amount of C-14 (100%).
No is the amount of C-14 left (100% - 46%).
t is the time you are looking for.
h is the half life.

Hm... radioactice decay in general. It is used in several fields.