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.

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.