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MK100
06.03.2021 •
Mathematics
The half life of a certain tranquilizer in the bloodstream is 36 hours. How long will it take for the drug to decay to 87% of the original dose? Use the exponential decay model to solve.
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Ответ:
Finding the Decay constant(λ):
λ = 0.693 / (half-life)
we are given that the half-life is 36 hours
λ = 0.693 / (36)
λ = 0.01925 /hour
Time taken for 87% decay:
Since decay is first-order, we will use the formula:
Where A₀ is the initial amount and A is the final amount
Let the initial amount be 100 mg,
the final amount will be 87% of 100
Final amount = 100*87/100 = 87 mg
Replacing the values in the equation:
t = 7.18 hours
We used 'hours' as the unit because the unit of the decay constant is '/hour'
Therefore, the drug will decay to 87% of initial dosage after 7.18 hours
Ответ:
8/9 * 1/6 =
8/54 which reduces to 4/27 of the book each day <===