Question

Plutonium-240 decays according to the function \[Q(t)=Q _{o}e ^{-kt}\] where Q represents the quantity remaining after t years and k is the decay constant, 0.00011.. How long will it take 36 grams of plutonium-240 to decay to 12 grams?. A. 18,900 years. B. 1.44 years. C. 9,990 years. D. 2,100 years.

Answer 1

C. 9,990 years is the correct answer

Answer 2

To answer the question above, substitute the given values to the given equation,
                                   Q(t) = Q x e^-kt
  
                          12 grams = (36 grams) x e^(-0.00011)(t)

Solving for t gives t = 9,987.38 years or approximately equal to 9,990 years. Thus, the answer is letter C.