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QUESTION 19 Carbon dating presumes that, as long as a plant or animal is alive, the proportion of its carbon that is C is constant. The amount of '*C in an object made from harvested plants, like paper, will decline exponentially according to the equation 4 = -0.00012134, where A represents the amount of Ic in the object, A, represents the amount ofc in living organisms, and is the time in years since the plant was harvested. If an archeological artifact has 35% as much as a living organism, how old would you predict it to be? Round to the nearest year a. 8655 years 6.93 years c 15,427 years d. 5715 years 0.29,310 years

Answer 1

A = A_o e^{- 0.0001213t}

Given, Amount of carbon left = 35 % of A_o = (35 / 100) * A_o = 0.35A_o

Let us assume the artifact is x years old

Therefore,

A_o e^{- 0.0001213x} = 0.35A_o

=> e^{- 0.0001213x} = 0.35A_o / A_o = 0.35

=> ln (e^{- 0.0001213x}) = ln (0.35)

=> - 0.0001213x = ln (0.35)

=> x = 8654.76 $\approx$ 8655

Therefore, The artifact is 8655 years old

Option (a) is the correct answer