Let be the amount of carbon-14 remaining at time t, let be the original amount of carbon-14. since we lose carbon-14 in an exponential decay, we have that:
where is the rate of decay and is the time elapsed.
now, we know that where is the half-life
thus we have:
now assume we have 1 unit to begin with. then the A remaining after 2000 years (in the decimal form of a percentage) is given by:
now calculate that