Question 277974
The redioactive isotope thorium 234 has a half-life of approximately 578 hours.
A(t) = Ao*(1/2)^(t/578)
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a) If a sample has an initial mass of 64 mg, a function that models the mass in mg after t hours is a(t)= 64*(1/2)^(t/578)
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b) The amount remaining after 75 hours will be about __________ mg.
A(75) = 64*(1/2)^(75/578)
A(75) = 64*0.914
A(75) = 58.5 mg
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c) The initial mass will decay to 12 mg after ________ hours. 
solve 12 = 64*(1/2)^(t/578)
(1/2)^(t/578) = 0.1875
Take the natural log of both sides to get:
(t/578)ln(1/2) = ln(0.1875)
t/578 = 2.4150
t = 1395.89 hrs.
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Cheers,
Stan H.