The halflife of a certain radioactive material is 68 hours A

The half-life of a certain radioactive material is 68 hours. An initial amount of the material has a mass of 641kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 4 hours. Round your answer to the nearest thousandth. y = 641(1/2)^68x; 0kg y = 1/2[1/641]^1/68^x; 0.342kg y = 641[1/2]^1/68x; 615.390 kg y = 2[1/641]^1/68x;1.367 kg Use the Change of Base Formula to evaluate log_373.

Solution

We know that

half life t_1/2 = In 2 /k

k = In2 / t_1/2

    = [ In 2] /68

Given that Initial amount Ao = 641 kg

Final amount y = Ao e^-kx     x = time

                     = (641) e^{-[In 2/68]x}

                       = (641) (1/2)^(1/68)x                            [ e^{-In 2} = 2^-1 = 1/2]

                       y = (641) (1/2)^(1/68)x

      After 4 hrs, remaining product will be

                 y = (641) (1/2)^(1/68)4

                 = 615.39 kg