SOLUTION: The half-life of a certain radioactive material is 68 hours. An initial amount of the material has a mass of 641 kg. Write an exponential function that models the decay of this mat
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-> SOLUTION: The half-life of a certain radioactive material is 68 hours. An initial amount of the material has a mass of 641 kg. Write an exponential function that models the decay of this mat
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Question 700923: The half-life of a certain radioactive material is 68 hours. An initial amount of the material has a mass of 641 kg. 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. Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! The half-life of a certain radioactive material is 68 hours. An initial amount of the material has a mass of 641 kg. 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.
.
General equation of exponential decay is:
A = Pe^(kt)
where
A is amount after time t
P is the initial amount (641)
k is a constant
t is time
.
Find k from:
"The half-life of a certain radioactive material is 68 hours."
.5 = e^(k*68)
ln(.5) = 68k
ln(.5)/68 = k
-0.0101933 = k
.
Our equation is now:
A = 641e^(-0.0101933t)
.
Now, we can answer:
"Find how much radioactive material remains after 4 hours."
A = 641e^(-0.0101933t)
A = 641e^(-0.0101933*4)
A = 641e^(-0.0407734)
A = 641(0.960046687)
A = 615.39 kg
