Question

Situation:Find the substance's half-life, in days.Round your answer to the nearest tenth.A 45 gram sample of a substance that'sused to sterilize surgical instruments hasa k-value of 0.15.Enter the correct answerN = Noe-ktDONENo = initial mass (at time t = 0)12N = mass at timetk = a positive constant that depends onthe substance itself and on the unitsused to measure timet = time, in days

Answer 1

Half life = 4.6 days

Step-by-step explanation

The amount of a material left is given as

N = N₀ e⁻ᵏᵗ

Where

Half-life is the time it takes a substance to reach half of its original value.

N₀ = Initial mass (at time t = 0) = 45 grams

N = mass at time = (45/2) = 22.5 grams

k = a positive constant that depends on the substance itself and on the units

used to measure time = 0.15 /day

t = time, in days = ?

N = N₀ e⁻ᵏᵗ

22.5 = 45 e⁻⁰.¹⁵ᵗ

Divide both sides by 45

(22.5/45) = e⁻⁰.¹⁵ᵗ

e⁻⁰.¹⁵ᵗ = 0.50

Take the natural logarithms of both sides

In e⁻⁰.¹⁵ᵗ = In 0.50

-0.15t = -0.693

Divide both sides by -0.15

(-0.15t/-0.15) = (-0.693/-0.15)

t = 4.6 days



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