The amount of carbon-14 present in animal bones t years after the animal's death is given by P (t) = - 0.00012097t. How old is an ivory tusk that has lost 34 % of its carbon-14?

I believe the equation you gave is wrong because the standard form of equation for C-14 decay is in the form of:

A = Ao e^-kt

So I think the right form of equation is (correct me if I’m wrong):

P (t) = Po e^ (-0.00012097t)

Where,

Po = initial value of C-14 at t = 0

t = time elapsed

Since it is given that:

P = (1 - 0.34) Po

P = 0.66 Po

Therefore, t is:

0.66 Po = Po e^ (-0.00012097 t)

0.66 = e^ (-0.00012097 t)

taking ln of both side:

ln 0. 66 = - 0.00012097 t

t = - ln 0. 66 / 0.00012097

t = 3,434.86 years

Therefore the ivory tusk is about 3,435 years old.