Albuterol is used to calm bronchospasm. It has a biological half-life of 7 hours and is normally inhaled as a 1.25 mg dose. (Note: Use the concepts of half-life or doubling time. The biological half-life of a substance is the amount of time it takes for the physiologic or radiologic activity of that substance to reduce by half.) Required:
a. Find a model for the amount of albuterol left in the body t hours after an initial dose of 1.25 mg.
b. How much albuterol is left in the body after 24 hours?

a. N(t) = 1.25 (1/2)^t/7

b. 0.1160933038mg.

Step-by-step explanation:

The formula for half life =

N(t) = No(1/2)^t/t½

Where N(t) = Amount of Substance left

No = Initial amount not Substance

t = time after t years

t½ = Half life of the substance

From the question:

No = 1.25mg

t½ = 7 years

a. Find a model for the amount of albuterol left in the body t hours after an initial dose of 1.25 mg.

N(t) = No(1/2)^t/t½

No = 1.25mg

t½ = 7 years

N(t) = 1.25 (1/2)^t/7

b. How much albuterol is left in the body after 24 hours?

Using the model in the above question

N(t) = 1.25 (1/2)^t/7

N(t) = 1.25(1/2)^24/7

N(t) = 1.25(0.5)^3.4285714286

N(t) = 0.1160933038mg

Therefore, the quantity of albuterol left in the body after 24 hours is 0.1160933038mg.

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