Introduction to Exponential Functions Checkpoint #3Checkpoint #3 Checkpoint 3: I can identify...
Transcript of Introduction to Exponential Functions Checkpoint #3Checkpoint #3 Checkpoint 3: I can identify...
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NAME DATE SECTION
IntroductiontoExponentialFunctionsCheckpoint#3
Checkpoint3:Icanidentifyfunctionrelationshipsandusefunctionnotationtodescribe&representandcalculatetheaveragerateofchange.1.Thegraphshowsthepopulationofbeaversinaforestfordifferentnumbersofyearsafter1995.Thebeaverpopulationisgrowingexponentially.
a. Explainwhywecanthinkofthebeaverpopulationasafunctionoftimeinyears.
b. Whatisthemeaningofthepointlabeledđinthiscontext?
c. Writeanequationusingfunctionnotationtorepresentthissituation.
2.Thegraphshowsthebacteriapopulationonapetridishasafunctionđthedaysđsinceanantibioticisintroduced.
1. Whatistheapproximatevalueofđ(4.5)?
2. Approximatelywhatisđwhenđ(đ) =400, 000?
Explainwhatyouwoulddo,usingyourusualgraphingtechnology,tobeabletoseeđ(15)onthegraph.
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3.HereisthefunctionđforClare'smoldybreadthatyousawearlier.
a. Whatistheaveragerateofchangeforthemoldoverthe6days?
b. Howwelldoestheaveragerateofchangedescribehowthemoldchangesforthese6days?
4.Aballisdroppedfromacertainheight.Thetableshowsthereboundheightsoftheballafteraseriesofbounces.
Fromwhatheight,approximately,doyouthinktheballwasdropped?Explainyourreasoning.
5.Herearethreegraphsrepresentingthreeexponentialfunctions,đ,đ,andâ.
Thefunctionsđandâaregivenbyđ(đ„) = 10 â 2!andâ(đ„) =20 â 4! .Whichofthefollowingcoulddefinethefunctionđ?Explainyourreasoning.
a. EquationA:đ(đ„) = 20 â (1.5)!
b. EquationB:đ(đ„) = 20 â (2.5)!
c. EquationC:đ(đ„) = 10 â (3.5)!
d. EquationD:đ(đ„) = 20 â (4.5)!
đ,timesincemoldspotting
(days)
đ(đ),areacoveredbymold(squaremillimeters)
0 11 22 43 84 165 326 64
bouncenumber heightincentimeters1 302 63 14 0
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6. Herearetwographsrepresentingthefunctionđgivenbyđ(đ„) = 10 â 2!andthefunctionđdefinedbyđ(đ„) = đ â đ! .
a. Isđgreaterthanorlessthan2?Explainhowyouknow.
b. Writeanequationthatdefinesđ.Showyourreasoning.
c. đandđrepresentthenumber,inthousands,ofsocialmediafollowersoftwoorganizationsasafunctionofyearssince2010.Whatdoestheintersectionofđandđmeaninthiscontext?