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  1. A radioactive substance decays exponentially. A scientist begins with 110 milligrams

of a radioactive substance. After 31 hours, 55 mg of the substance remains. How

many milligrams will remain after 42 hours?

Verified Answer :

foggles

Firstly set up the equation as so:
R = me^(-λt)
From the initial conditions: 
 110 = me^(-λ0)
∴ m = 110

From the other piece of information:
55 = 110e^(-λ31)
55/110 = e^(-31λ)
∴ -ln(2) = -31λ
λ = ln(2)/31

Therefore:
R = 110e^(42*(-ln(2)/31))
∴ R ≈ 43 mg

(ln(x) is the natural log of x)

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