# Pre-calculus

Initially 600 milligrams of a radioactive substance was present. After 7 hours the mass had decreased by 3%. Construct an exponential model
A(t) = A0ekt for the amount remaining of the decaying substance after t hours. Find the amount remaining after 24 hours.

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1. so
600(.97) = 600 e^(7k)
.97 = e^(7k)
ln .97 = 7k lne
7k = ln .97
k = ln .97/7 = -.004351315

amount = 600 e^-.0043511315t
so when t = 24
amount = 600 e^-.104431..
= .900836(600) ----> 90.08% remain
= 540.50 mg

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posted by Reiny

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