# Half-life

• Sep 22nd 2009, 11:32 AM
mikegar813
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.
• Sep 22nd 2009, 11:45 AM
skeeter
Quote:

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.

$y = y_0 \left(\frac{1}{2}\right)^{\frac{t}{5730}}$

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

solve for $t$
• Sep 22nd 2009, 11:48 AM
Calculus26
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
• Sep 22nd 2009, 11:52 AM
mikegar813
i got 13304.6 years does this sound right?

t= (-5730(ln 0.2))/(ln 2)
• Sep 22nd 2009, 12:40 PM
Calculus26
yes but in reality you wouldn't claim that much accuracy--It would probably be claimed as about 13,000 years