SOLUTION: The half-life of a certain radioactive material is 85 days. An initial amount of material has a mass of 801 kg. Write an exponential function that models the decay of this material

Question 551354: The half-life of a certain radioactive material is 85 days. An initial amount of material has a mass of 801 kg. Write an exponential function that models the decay of this material.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
exponential delay form:
N = Noe^(kt)
where
N is amount after time t
No is initial amount
k is a constant (<0)
.
The half-life of a certain radioactive material is 85 days. An initial amount of material has a mass of 801 kg. Write an exponential function that models the decay of this material.
.
Here, all we need to do is the define 'k' -- do this with the info provided and plug into:
N = Noe^(kt)
(1/2)(801) = 801e^(k*85)
dividing both sides by 801:
(1/2) = e^(k*85)
ln(1/2) = k*85
ln(1/2)/85 = k
-.0082 = k
.
So, the exponential decay model is
N = 801e^(-.0082t)

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