A particular compound decays according to the equation y=ae^-0.0736t, where t is in days.  Find the half life of the compound.

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ncchemist | eNotes Employee

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The equation for exponential decay is:

N(t) = N(0)e^(-L*t)

where N(t) is the amount of substance left after t amount of time, N(0) is the amount of substance originally started with when t=0, L is called the decay constant that is specific to the particular substance decaying, and t is the amount of time that has passed. You have given the equation:

y=ae^(-0.0736t)

So the equation fits the general form with 0.0736 as the decay constant and "a" as N(0). By definition, at the half life half of the substance will be consumed. So at the half life, t will be denoted by t(1/2), and y will be equal to a/2.

a/2 = ae^(-0.0736*t(1/2))

1/2 = e^(-0.0736*t(1/2))

ln(1/2) = -0.0736*t(1/2)

ln(1/2)/-0.0736 = t(1/2) = 9.42 days

So the answer is the half life of the compound is 9.42 days.

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