NAME DATE SECTION Introduction to Exponential Functions Checkpoint #3 Checkpoint 3: I can identify function relationships and use function notation to describe & represent and calculate the average rate of change. 1. The graph shows the population of beavers in a forest for different numbers of years after 1995. The beaver population is growing exponentially. a. Explain why we can think of the beaver population as a function of time in years. b. What is the meaning of the point labeled in this context? c. Write an equation using function notation to represent this situation. 2. The graph shows the bacteria population on a petri dish as a function the days since an antibiotic is introduced. 1. What is the approximate value of (4.5)? 2. Approximately what is when () = 400, 000? Explain what you would do, using your usual graphing technology, to be able to see (15)on the graph.
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NAME DATE SECTION
IntroductiontoExponentialFunctionsCheckpoint#3
Checkpoint3:Icanidentifyfunctionrelationshipsandusefunctionnotationtodescribe&representandcalculatetheaveragerateofchange.1.Thegraphshowsthepopulationofbeaversinaforestfordifferentnumbersofyearsafter1995.Thebeaverpopulationisgrowingexponentially.
a. Explainwhywecanthinkofthebeaverpopulationasafunctionoftimeinyears.
b. Whatisthemeaningofthepointlabeled𝑄inthiscontext?
c. Writeanequationusingfunctionnotationtorepresentthissituation.
2.Thegraphshowsthebacteriapopulationonapetridishasafunction𝑓thedays𝑑sinceanantibioticisintroduced.
1. Whatistheapproximatevalueof𝑓(4.5)?
2. Approximatelywhatis𝑑when𝑓(𝑑) =400, 000?
Explainwhatyouwoulddo,usingyourusualgraphingtechnology,tobeabletosee𝑓(15)onthegraph.
3.Hereisthefunction𝑓forClare'smoldybreadthatyousawearlier.
a. Whatistheaveragerateofchangeforthemoldoverthe6days?
b. Howwelldoestheaveragerateofchangedescribehowthemoldchangesforthese6days?
4.Aballisdroppedfromacertainheight.Thetableshowsthereboundheightsoftheballafteraseriesofbounces.
Fromwhatheight,approximately,doyouthinktheballwasdropped?Explainyourreasoning.
5.Herearethreegraphsrepresentingthreeexponentialfunctions,𝑓,𝑔,andℎ.
Thefunctions𝑓andℎaregivenby𝑓(𝑥) = 10 ⋅ 2!andℎ(𝑥) =20 ⋅ 4! .Whichofthefollowingcoulddefinethefunction𝑔?Explainyourreasoning.
a. EquationA:𝑔(𝑥) = 20 ⋅ (1.5)!
b. EquationB:𝑔(𝑥) = 20 ⋅ (2.5)!
c. EquationC:𝑔(𝑥) = 10 ⋅ (3.5)!
d. EquationD:𝑔(𝑥) = 20 ⋅ (4.5)!
𝑑,timesincemoldspotting
(days)
𝑓(𝑑),areacoveredbymold(squaremillimeters)
0 11 22 43 84 165 326 64
bouncenumber heightincentimeters1 302 63 14 0
6. Herearetwographsrepresentingthefunction𝑓givenby𝑓(𝑥) = 10 ⋅ 2!andthefunction𝑔definedby𝑔(𝑥) = 𝑎 ⋅ 𝑏! .
a. Is𝑏greaterthanorlessthan2?Explainhowyouknow.
b. Writeanequationthatdefines𝑔.Showyourreasoning.
c. 𝑓and𝑔representthenumber,inthousands,ofsocialmediafollowersoftwoorganizationsasafunctionofyearssince2010.Whatdoestheintersectionof𝑓and𝑔meaninthiscontext?
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