2. A patient is discharged from a hospital, but needs to be given a drug to take

Question

2. A patient is discharged from a hospital, but needs to be given a drug to take every week to treat his condition. A doctor considers several different dosage schedules, each which would lead to a different amount of the drug present in the patient's system. The following functions indicate the amount of drug which would be present in the patient's system after t weeks under four proposed dosage schedules, where the output of each function is the portion of a lethal dose present (for example, an output of .2 would indicate that the patient has 20% of a lethal dose). 4t , p2(t) =-, ps(t) = t +1 t 20 t2 +1 The doctor knows that the dosage schedule must satisfy the following properties: The value of the function should never be equal to or greater than 1 for positive values of t, since that would kill the patient. To be effective, the value after 1 week must be at least 4. The drug should eventually leave the patient's system. That is, the limit of the function as approaches oo should be 0. After reviewing the four functions, the doctor sees that only one of them meets the necessary properties. Find it, and indicate why the other three functions do not meet the necessary properties

Explanation / Answer

At t= 2 , p1(2) = 4×2/ (2-3)^2 = 8 > 1 rejected

At t = 1 , p3(1) = 1/1+20 = 1/21 < 0.4 rejected

As t tends to infinity p2(t) = 1 , rejected

Therefore p4(t) is the correct option.

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