How long will it take a sample of radioactive substance to decay to half of its original amount, if it decays according to the function A(t)=550e^-0.158t, where t is the time in years? ROund to the nearest hundredth year.
At t = 0, A(0) = 550 years
Half of this occurs when 550/2 = 550*e^(-0.158t)
1/2 = e^(-0.158t)
ln(1/2) = -0.158t
-ln(2) = -0.158t
t = ln(2)/0.158 years = 4.387 years ot t = 4.39 years to the nearest hundredth of a year.
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