Anyone know how to go about solving a problem like this?
Yesterday the Holy Grail was found in my lawn. Knowing the Grail must be 2,000 yrs old and Carbon-14's 1/2 Life is 5,700 yrs, what % must be gone to be real
What a coincidence! i found the Grail in my backyard just last week. mine is the real one of course.
Let $\displaystyle A(t)$ be the amount of carbon-14 remaining at time t, let $\displaystyle A_0(t)$ be the original amount of carbon-14. since we lose carbon-14 in an exponential decay, we have that:
$\displaystyle A = A_0e^{-rt}$
where $\displaystyle r$ is the rate of decay and $\displaystyle t$ is the time elapsed.
now, we know that $\displaystyle r = \frac {\ln 2}{t_h}$ where $\displaystyle t_h$ is the half-life
thus we have:
$\displaystyle A = A_0e^{\frac {\ln 2}{5700}t}$
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:
$\displaystyle A = e^{\frac {\ln 2}{5700}(2000)}$
now calculate that