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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IntroductiontoExponentialFunctionsCheckpoint#3
Checkpoint3:Icanidentifyfunctionrelationshipsandusefunctionnotationtodescribe&representandcalculatetheaveragerateofchange.1.Thegraphshowsthepopulationofbeaversinaforestfordifferentnumbersofyearsafter1995.Thebeaverpopulationisgrowingexponentially.
a. Explainwhywecanthinkofthebeaverpopulationasafunctionoftimeinyears.
b. Whatisthemeaningofthepointlabeledđť‘„inthiscontext?
c. Writeanequationusingfunctionnotationtorepresentthissituation.
2.Thegraphshowsthebacteriapopulationonapetridishasafunctionđť‘“thedaysđť‘‘sinceanantibioticisintroduced.
1. Whatistheapproximatevalueofđť‘“(4.5)?
2. Approximatelywhatisđť‘‘whenđť‘“(đť‘‘) =400, 000?
Explainwhatyouwoulddo,usingyourusualgraphingtechnology,tobeabletoseeđť‘“(15)onthegraph.
3.Hereisthefunctionđť‘“forClare'smoldybreadthatyousawearlier.
a. Whatistheaveragerateofchangeforthemoldoverthe6days?
b. Howwelldoestheaveragerateofchangedescribehowthemoldchangesforthese6days?
4.Aballisdroppedfromacertainheight.Thetableshowsthereboundheightsoftheballafteraseriesofbounces.
Fromwhatheight,approximately,doyouthinktheballwasdropped?Explainyourreasoning.
5.Herearethreegraphsrepresentingthreeexponentialfunctions,đť‘“,đť‘”,andâ„Ž.
Thefunctionsđť‘“andâ„Žaregivenbyđť‘“(đť‘Ą) = 10 â‹… 2!andâ„Ž(đť‘Ą) =20 â‹… 4! .Whichofthefollowingcoulddefinethefunctionđť‘”?Explainyourreasoning.
a. EquationA:đť‘”(đť‘Ą) = 20 â‹… (1.5)!
b. EquationB:đť‘”(đť‘Ą) = 20 â‹… (2.5)!
c. EquationC:đť‘”(đť‘Ą) = 10 â‹… (3.5)!
d. EquationD:đť‘”(đť‘Ą) = 20 â‹… (4.5)!
đť‘‘,timesincemoldspotting
(days)
đť‘“(đť‘‘),areacoveredbymold(squaremillimeters)
0 11 22 43 84 165 326 64
bouncenumber heightincentimeters1 302 63 14 0
6. Herearetwographsrepresentingthefunctionđť‘“givenbyđť‘“(đť‘Ą) = 10 â‹… 2!andthefunctionđť‘”definedbyđť‘”(đť‘Ą) = đť‘Ž â‹… đť‘Ź! .
a. Isđť‘Źgreaterthanorlessthan2?Explainhowyouknow.
b. Writeanequationthatdefinesđť‘”.Showyourreasoning.
c. đť‘“andđť‘”representthenumber,inthousands,ofsocialmediafollowersoftwoorganizationsasafunctionofyearssince2010.Whatdoestheintersectionofđť‘“andđť‘”meaninthiscontext?