Transcript Drugs in the Body (1)

Drugs in the Body (1)
Recurrence Relations
Drugs in the Body
A patient is given an initial dose of 50mg of a drug.
Each hour the patient is given a 20mg tablet of the drug.
The drug has a decay factor of 70% ie. every 20 minutes ,
70% of the drug remains in the body.
Set up a recurrence relation and use it
to determine the long term state of the drug in the body.
Drugs in the Body
A patient is given an initial dose of 80mg of a drug.
This drug is given in tablet form as 30mg tablets every hour.
The drug has a decay factor of 85% ie. every 15 minutes , 85% of the drug
present in the body at the start
of the 15 minute interval remains in the body.
Set up a recurrence relation and use
it to determine the long term state of the drug in the body.
Drugs in the Body
Initial dose : 120mg
Tablet : 40 mg tablet given every hour.
Decay factor : The drug has a decay factor of 68%
ie. every 30 minutes ,
68% of the drug present in the body at the start
of the 30 minute interval remains in the body.
Set up a recurrence relation and use it to
determine the long term state of the drug in the body.
Solutions
Drugs in the Body (1)
Q1. An+1=0.343An + 20, A0 = 50
Limit: L = 30.44 grams
Q2. An+1=0.522An + 30, A0 = 80
Limit: L = 62.76 grams
Q3. An+1=0.4624An + 40, A0 = 120
Limit: L = 74.4 grams