The following HTML text is provided to enhance online
readability. Many aspects of typography translate only awkwardly to HTML.
Please use the page image
as the authoritative form to ensure accuracy.
column and the ''total in system" column may then be represented as shown in Table 3, which can easily be converted into a spreadsheet. Table 3 also suggests the recursion equation: .4An - 1 + 440 = An, where An is the amount of drug present at the beginning of the nth 8-hour period (or nth dose).
TABLE 1: Calculation of amount of drug in system
DAY
TIME IN HOURS
DRUG REMAINING
+ AMOUNT TAKEN
= TOTAL IN SYSTEM
1
0
0
+ 440
= 440
1
8
176
+ 440
= 616
1
16
246.40
+ 440
= 686.4
2
24
274.56
+ 440
= 714.56
TABLE 2: Calculation of amount of drug in system, first generalization
DOSE n
DRUG REMAINING
+ AMOUNT TAKEN
= TOTAL IN SYSTEM,
An
1
0
+ 440
= 440
A1
2
(.4)(440)
+ 440
= 616
A2
3
(.4)(616)
+ 440
= 686.4
A3
4
(.4)(686.4)
+ 440
=7 14.56
A4
TABLE 3: Calculation of amount of drug in system, second generalization
DOSE n
DRUG REMAINING
+ AMOUNT TAKEN
= TOTAL IN SYSTEM,
An
1
0
+ 440
= A1
2
(.4)A1
+ 440
= A2
3
(.4)A2
+ 440
= A3
4
(.4)A3
+ 440
= A4
More advanced students might begin their solutions by modeling the process with this recursion equation, expressing the relationship between An - 1 and An. Such an equation is well suited for use in a programmable calculator or a spreadsheet, especially in investigating the long-term behavior of the model.