Answer
It is quite possible to use potassium-40 to date a dinosaur fossil to 68 million years old since this age is much less than the half-life of potassium-40.
The maximum age of a fossil that could be dated using potassium-40 is 12.46 billion years which is much older than the earth and almost as old as the universe.
Work Step by Step
We can find the value of $k$ when we use potassium dating:
$m(t) = m(0)e^{kt}$
$m(1.25) = m(0)e^{1.25k} = 0.5~m(0)$
$e^{1.25k} = 0.5$
$1.25~k = ln(0.5)$
$k = \frac{ln(0.5)}{1.25}$
$k = -0.554518$
Then:
$m(t) = m(0)~e^{-0.554518~t}$
We can find the time $t$ when only 0.1% remains:
$m(t) = m(0)~e^{-0.554518~t} = 0.001~m(0)$
$e^{-0.554518~t} = 0.001$
$(-0.554518)~t = ln(0.001)$
$t = \frac{ln(0.001)}{-0.554518}$
$t = 12.46~$ billion years
It is quite possible to use potassium-40 to date a dinosaur fossil to 68 million years old since this age is much less than the half-life of potassium-40.
The maximum age of a fossil that could be dated using potassium-40 is 12.46 billion years which is much older than the earth and almost as old as the universe.
