Spreadsheet: 0ac2a87d-ac0e-411e-ad92-a175731025f0
Sheet: Sheet1

Initial dose is 30mg. Regular dose is 10 mg, taken at the end of each time period. | Unnamed: 1 | Unnamed: 2 | Unnamed: 3 | Unnamed: 4
20% is eliminated each time period. How much drug in body after number of time periods?
Construct, explain, and analyze models.
Period | Reduce by 20% before the dose. Find amount after each dose. | Reduce by 20% before the dose. Find amount before each dose. | Reduce by 20% after the dose. Find amount after each dose. | Take dose at start of time period. Find amount at end of each time period.
 | NEXT=.8NOW+10 | Period1=.8*initial; NEXT=.8(NOW+10) | NEXT=.8(NOW+10) | NEXT=.8(NOW+10)
 | 30 | 30 | 30 | 30
1 | 34 | 24 | 32 | 32
2 | 37.2 | 27.2 | 33.6 | 33.6
3 | 39.76000000000001 | 29.76000000000001 | 34.88 | 34.88
4 | 41.80800000000001 | 31.80800000000001 | 35.904 | 35.904
5 | 43.4464 | 33.4464 | 36.72320000000001 | 36.72320000000001
6 | 44.75712000000001 | 34.75712000000001 | 37.37856000000001 | 37.37856000000001
7 | 45.805696 | 35.805696 | 37.90284800000001 | 37.90284800000001
8 | 46.6445568 | 36.6445568 | 38.32227840000001 | 38.32227840000001
9 | 47.31564544 | 37.31564544 | 38.65782272000001 | 38.65782272000001
10 | 47.852516352 | 37.852516352 | 38.92625817600001 | 38.92625817600001
11 | 48.28201308160001 | 38.28201308160001 | 39.14100654080001 | 39.14100654080001
12 | 48.62561046528 | 38.62561046528 | 39.31280523264002 | 39.31280523264002
13 | 48.900488372224 | 38.900488372224 | 39.45024418611202 | 39.45024418611202
14 | 49.12039069777921 | 39.12039069777921 | 39.56019534888961 | 39.56019534888961
15 | 49.29631255822337 | 39.29631255822337 | 39.6481562791117 | 39.6481562791117
16 | 49.4370500465787 | 39.4370500465787 | 39.71852502328936 | 39.71852502328936
17 | 49.54964003726296 | 39.54964003726296 | 39.77482001863149 | 39.77482001863149
18 | 49.63971202981037 | 39.63971202981037 | 39.81985601490519 | 39.81985601490519
19 | 49.7117696238483 | 39.7117696238483 | 39.85588481192416 | 39.85588481192416
20 | 49.76941569907864 | 39.76941569907864 | 39.88470784953932 | 39.88470784953932
21 | 49.81553255926292 | 39.81553255926292 | 39.90776627963146 | 39.90776627963146
22 | 49.85242604741034 | 39.85242604741034 | 39.92621302370517 | 39.92621302370517
23 | 49.88194083792828 | 39.88194083792828 | 39.94097041896414 | 39.94097041896414
24 | 49.90555267034262 | 39.90555267034262 | 39.95277633517131 | 39.95277633517131
25 | 49.9244421362741 | 39.9244421362741 | 39.96222106813705 | 39.96222106813705
26 | 49.93955370901929 | 39.93955370901929 | 39.96977685450965 | 39.96977685450965
27 | 49.95164296721543 | 39.95164296721543 | 39.97582148360772 | 39.97582148360772
28 | 49.96131437377235 | 39.96131437377235 | 39.98065718688618 | 39.98065718688618
29 | 49.96905149901789 | 39.96905149901789 | 39.98452574950895 | 39.98452574950895
30 | 49.97524119921431 | 39.97524119921431 | 39.98762059960716 | 39.98762059960716
31 | 49.98019295937145 | 39.98019295937145 | 39.99009647968573 | 39.99009647968573
32 | 49.98415436749716 | 39.98415436749716 | 39.99207718374859 | 39.99207718374859
33 | 49.98732349399774 | 39.98732349399774 | 39.99366174699887 | 39.99366174699887
34 | 49.98985879519819 | 39.98985879519819 | 39.9949293975991 | 39.9949293975991
35 | 49.99188703615855 | 39.99188703615855 | 39.99594351807929 | 39.99594351807929
36 | 49.99350962892684 | 39.99350962892684 | 39.99675481446343 | 39.99675481446343
37 | 49.99480770314148 | 39.99480770314148 | 39.99740385157074 | 39.99740385157074
38 | 49.99584616251318 | 39.99584616251318 | 39.9979230812566 | 39.9979230812566
39 | 49.99667693001055 | 39.99667693001055 | 39.99833846500528 | 39.99833846500528
40 | 49.99734154400844 | 39.99734154400844 | 39.99867077200423 | 39.99867077200423
41 | 49.99787323520675 | 39.99787323520675 | 39.99893661760339 | 39.99893661760339
42 | 49.9982985881654 | 39.9982985881654 | 39.99914929408271 | 39.99914929408271
43 | 49.99863887053233 | 39.99863887053233 | 39.99931943526617 | 39.99931943526617
44 | 49.99891109642586 | 39.99891109642586 | 39.99945554821294 | 39.99945554821294
45 | 49.99912887714069 | 39.99912887714069 | 39.99956443857036 | 39.99956443857036
46 | 49.99930310171256 | 39.99930310171256 | 39.99965155085629 | 39.99965155085629
47 | 49.99944248137005 | 39.99944248137005 | 39.99972124068503 | 39.99972124068503
48 | 49.99955398509604 | 39.99955398509604 | 39.99977699254803 | 39.99977699254803
 | Compare 1 and 2 – Mainly just record-keeping difference, either record the amt
 | just after the dose (1), or record the amt just before the dose (2). Note that (1) is
 | always exactly 10 more than (2). Which is correct? Could go with either, with
 | explanation. In terms of what is happening in the body, in the long term, the amt
 | is oscillating between about 40 and about 50. So either model is plausible, taken
 | together they give additional insight. Also see attached Two Models graphic.
 | Model 3 – This implies losing 20% immediately after taking the dose. Not realistic.
 | Model 4 – This requires taking the dose at the beginning of each time period,
 | including the initial time period, which means that the initial amount is 40.
 | This does not match the statement of the problem.
 | Compare 1, 2, and 3:
 | Start | 30
 | Lose 20% over time | 24
 | Add 10 | 34
 | Record Amount |  | .8(NOW) + 10
 | Start | 30
 | Lose 20% over time | 24
 | Record | 24
 | Add 10 | 34
 | Lose 20% over time | 27.2
 | Record Amount |  | .8(NOW + 10)
 | Start | 30
 | Add 10 | 40
 | Lose20%immediately | 32
 | Record Amount |  | .8(NOW + 10)