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High School Mathematics at Work: Essays and Examples for the Education of All Students (1998)
Mathematical Sciences Education Board (MSEB)

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81
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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.

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