The amount of carbon 14 present after t years is given by th

The amount of carbon 14 present after t years is given by the exponential equation A(t) = A_0 e^kt, with k = - ln 2/5600. Using carbon 14 dating of charcoal found along with fossilized leaf fragments, botanists arrived at an age of 42.000 years for a plant. What percent of the original carbon 14 in the charcoal was present? % the original carbon 14 in the charcoal was present. (Round to the nearest tenth as needed.)

Solution

A(t) = Aoe^kt) where k = -ln2/5600 = -0.00012377 per year

time , t = 42000

So, A(42000) = Aoe^(-0.00012377*42000)

= Ao(0.0055)

% of original charcoal = [(Ao(0.0055))/Ao]*100 = 0.55 = 0.6%