<PRE><B>Question 133943</B>
How long does it take 12 grams of carbon-14 to decay to 10 grams when the decay is exponential with an annual rate of decay of 0.0124%?
:
Using the decay equation:
12 * (1-.000124)^t = 10
:
.999876^t = {{{10/12}}}
:
log(.999876^t) = log({{{10/12}}}); divided both sides by 12, using logs
:
t*log(.999876) = log({{{10/12}}}); using log equiv of exponents
:
-.00005385t = -.07918; find the actual logs
t = {{{(-.07918)/(-.00005385)}}}
t = 1,470 years
:
:
Check on a calc, enter: 12(1-.000124)^1470 = 10.000</PRE>