SOLUTION: The amount of carbon-14 located in animal bones after t years is given by P(t)=Poe^-0.00012t a bone has lost 19% of its carbon-14 how old is the bone? How old is a bone that has lo

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: The amount of carbon-14 located in animal bones after t years is given by P(t)=Poe^-0.00012t a bone has lost 19% of its carbon-14 how old is the bone? How old is a bone that has lo      Log On


   

Question 618620: The amount of carbon-14 located in animal bones after t years is given by P(t)=Poe^-0.00012t a bone has lost 19% of its carbon-14 how old is the bone? How old is a bone that has lost 23%?
Answer by nerdybill(7384) About Me  (Show Source):
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The amount of carbon-14 located in animal bones after t years is given by P(t)=Poe^-0.00012t a bone has lost 19% of its carbon-14 how old is the bone?
.
P(t)=Poe^-0.00012t
(1-.19)Po = Poe^(-0.00012t)
.81Po = Poe^(-0.00012t)
dividing both sides by Po:
.81 = e^(-0.00012t)
take ln of both sides:
ln(.81) = -0.00012t
ln(.81)/(-0.00012) = t
1756 years = t
.
How old is a bone that has lost 23%?
P(t)=Poe^-0.00012t
(1-.23)Po = Poe^(-0.00012t)
(.77)Po = Poe^(-0.00012t)
dividing both sides by Po:
.77 = e^(-0.00012t)
take ln of both sides:
ln(.77) = -0.00012t
ln(.77)/(-0.00012) = t
2178 years = t