1.If30%Of Sneeze-B-Gone Hasflushed out of Thebody After 24 Hours,What

PartA

Haveyou ever taken a medication that yourdoctor warned you would not take effect forafewdays?Inthisactivity,youwillinvestigatewhythat isthecase.

ConsidertheallergymedicineSneeze-B-Gone.Theregularadultdoseis20milligrams.Aswithallmedicines,thebodygraduallyfiltersSneeze-B-Goneoutofthebloodstream.Therateat which the medicine is filtered outis called theflush rate. For Sneeze-B-Gone, theflushrateis30%.Inotherwords, 24hoursafterthe pillistaken,30%ofSneeze-B-Gonehasflushedoutofthebody.

1.If30%of Sneeze-B-Gone hasflushed out of thebody after 24 hours,what percentofSneeze-B-Goneremains?

2.Useyourcalculator’srecursionfeaturetofillinthetablebelow,assumingthatanadult istakingone20-milligramdoseperday.

3.At what valuedoes the amount ofSneeze-B-Goneinthebloodstreamleveloff?How manydays does ittake for that tohappen?

4.Whattypeoffunctioncould modeltheamountofSneeze-B-Goneinthebloodstreamasafunction oftime?Explainyourchoice.

5.WhatwouldyouexpectagraphoftheamountofSneeze-B-Goneinthebloodstreamasafunction oftimetolooklike?Explainyourprediction.

6.Recallthatthegeneralformforexponentialdecayfunctionsisy=a(b)x,where arepresentsthestartingamountofthesubstanceandbrepresentsthe rate ofdecay. Fora20-milligram doseanda30%flushrate,whatexponentialfunctioncoulddescribetheamountofSneeze-B-Gonein thebloodstream(y)asafunctionoftime (x)?(Donotforgetthatbrepresentsthepercentof Sneeze-B-Gonethatremains inthebloodstream.)

7.Since the patient didnot begintaking themedicine untilDay 1, adjustyour function rulebysubtracting1fromtheexponent.Graphthefunctiononyourgraphingcalculator. Sketchyourgraphanddescribeyourviewingwindow.

8.Iftime (x)isgivenintermsofthenumberofdays,whathappenstotheamountofSneeze-B-Gonein the patient’sbloodstream at the start of Day2when the patienttakesasecondpill?Howdoesthisaffectthegraph?

9.Use what you learned aboutstep and piecewise functions in previous activitiesto restrictthedomainofthegraph.Sketchyournewgraph.

10.For Day2,enterthe functiony 340.7x1 intoyourcalculator. Whatdo theconstants34,0.7,and2represent?Sketchthenew graph.

11.Basedonthe functions for Day1 andDay2, write a function fromthe datain your tableforDay3anda functionforDay4.

12.Graphbothofthesenewfunctions.Whatpatternsdoyounotice?Whatdoyouexpect thegraphforDay5tolooklike?

13.TestyourpredictionbywritingafunctionforDay5.

14.REFLECTION:Assumethepatienttakes20milligramsofSneeze-B-Goneeveryday.IfyouextendthegraphtoDay20orbeyond,whatwouldtheminimumamountofSneeze-B-Goneinthebloodstreambe?Themaximumamount?

PartB

1.Supposeapatientrequiresa 30-milligramdoseofSneeze-B-

Gone.Usehomescreenrecursiononyour calculator to fillinthetable.

2.At what valuedoes the amount ofSneeze-B-Goneinthebloodstreamleveloff?How manydays does ittake for that tohappen?

3.Howdoesthefunction ruleforthe20-milligramdosechangefora

30-milligramdose?Writethenew functionrule fortheportionofthegraphbetween Day1 and Day2.

4.Howdoyouthinkthosechangeswouldaffectthegraphofthenew function rule?

5.Useyourgraphingcalculatortotest yourprediction.Sketchyourgraph.

6.WhentheamountofSneeze-B-Goneinthebloodstreamlevelsoffforapatienttakinga30-milligramdailydose,whataretheminimumandmaximumamountsofSneeze-B-Goneinthebloodstreamwithinagivenday?

7.Supposeapatientrequiresa40-milligram doseof Sneeze-B-Gone.Basedon whatyouhaveobservedsofar,whatwouldyouexpectthefunctionruleandgraphtolooklike?

8.Userecursiononyour calculatortofill inthe table.

9.At what valuedoes the amount ofSneeze-B-Goneinthebloodstreamleveloff?How manydays does ittake for that to happen? You mayneedtoextendthe valuesinthe table.

10.Howdoesthefunctionruleforthe30-milligramdosechangewitha40-milligramdose?Writethe new function rule for theportionofthegraphbetween Day 1 andDay2.

11.Howdoyouthinkthosechangeswouldaffectthegraphofthenew function rule?

12.Useyourgraphingcalculatortotestyourprediction.Sketchyourgraph.

13.WhentheamountofSneeze-B-Goneinthebloodstreamlevelsoffforapatienttakinga40-milligramdose,whataretheminimumandmaximumamountsofSneeze-B-Gone inthebloodstreamwithinagivenday?

14.REFLECTION:HowdoesanincreaseindoseaffecttheamountofSneeze-B-Goneinthebloodstreamwhenthe amountlevelsoff?

15.Fillin thetable below.What relationshipsdo younotice?

Dose / FlushRate / Leveled-offAmount / DoseFlushRate
20
30
40

16.REFLECTION:If you werea doctor ornurse and youknew that apatientneeded tohaveabout100milligramsofSneeze-B-Goneinhisbloodstreamforthemedicinetobeeffective,whatdosewouldyouprescribe?Explainyourdecision.

17.EXTENSION:Anewcholesterol-loweringmedicinehasaflushrateof50%.Fora

20-milligramdoseofthismedicine,howdothefunctionrulesandgraphcomparetothoseforthe 20-milligramdoseofSneeze-B-Gone witha flushrate of30%?Use yourgraphingcalculatortoinvestigate.Presentyourworktotheclass.