Word Problem Algebra for Calculus

Question

The amount of carbon-14 present in animal bones after t years is given by , a bone has lost 34% of it's carbon-14, How old are the bones?

Answer 1

P(t) = P₀·e^-0.00012t

P/P₀ = e^-0.00012t

P(t) is the amount remaining, not the amount lost. So if 34% has been lost, then 100% - 34% = 66% remains; that is P(t) = 0.66P₀ and P(t)/P₀ = 0.66.

0.66 = e^-0.00012t

ln(0.66) = -0.00012t

ln(0.66)/(-0.00012) = t

Use your calculator to get the answer.