1. ## Half-life

In the skull of an animal found in an archaeological dig, it was determined that about 20% of the original amount of carbon-14 was still present. If the half-life of carbon-14 is 5730 years, find the approximate age of the animal.

2. Originally Posted by mikegar813
In the skull of an animal found in an archaeological dig, it was determined that about 20% of the original amount of carbon-14 was still present. If the half-life of carbon-14 is 5730 years, find the approximate age of the animal.
$\displaystyle y = y_0 \left(\frac{1}{2}\right)^{\frac{t}{5730}}$

$\displaystyle 0.2 = \left(\frac{1}{2}\right)^{\frac{t}{5730}}$

solve for $\displaystyle t$

3. Let Q(t) denote the amount of C-14

For all half-life prblms

Q(t) = Q(0) e^(-kt)

Where k = ln(2)/halflife

k= ln(2)/5730 = .00012

Q(t) = Q(0) e^(-.00012t)

solve Q(t) = .2Q(0) = Q(0) e^(-.00012t) for t

.2 = e^(-.00012t)

I'll let you finish

4. i got 13304.6 years does this sound right?

t= (-5730(ln 0.2))/(ln 2)

5. yes but in reality you wouldn't claim that much accuracy--It would probably be claimed as about 13,000 years