Question

The amount of carbon-14 in animal bones after t years is given by P(t)=P[0]e^(-0.00012097t). A bone has lost 37% of its carbon-14. How old is the bone?

Answer 1

Step 1: Plug in 5,730 for t and modify P[0] so that P(t) is 50.

Answer 2

I would just use an arbitrary value for the initial amount, say 100, and then the amount remaining is the one given by that function. Since 37% has been lost then there is 67% left so
\[67=100*\exp(-0.0001209t)\]
and solve for t

Answer 3

63 remains sorry about that