Question

The drug Valium is eliminated from the bloodstream exponentially with a half-life of 36 hours. Suppose that a patient receives an initial dose of 75 milligrams of valium at midnight. 

a. How much valium is in the patient's blood at noon the next day?
b. Estimate when the Valium concentration will reach 35
% of its initial level. 
Please step by step

Answer 1

A = 75(1/2) ^ (24/36)

75 (1/2) ^ (2/3)

A = 47.2470 mg after 1 day.

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35% of 75 is 26.25 mg, so

26.25 = 75(1/2) ^ (24/?)

26.25^(x/24) = 75 ((.5)

24root(26.25^x) = 37.5

Ignore this second part I don't know how to do. part a is correct.

Answer 2

Part a : After next day in noon it will be 59.53 mg

Part b : After 52.53 hours it will be 35 % of initial

Explanation:

Equation is given by

A = 75(0.5)
`A=75 (0.5)^(t)/(36)`

initial dose at midnight

Part (a) then at noon next day means 12 hrs ,plugging t = 12 here ,we get

`A=75(0.5)^(12)/(36)`

A=75(0.5)
`A=75(0.5)^(1)/(3)`

on simplifying it ,we get

A =75(0.7937)

A=59.53 mg

Part (b) : 35 % of initial level means A = 0.35 of initial= 0.35 (75 )

`(0.35)(75) = 75 (0.5)^(t)/(36)`

`(0.35) = (0.5)^(t)/(36)`

t = 54.53 hours

After 54.53 hours it will remain 35% of initial amount