Lesson87AnswerKeyPrecalculusMathMedic7c83e031af

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Tampa Bay Tech High School**We aren't endorsed by this school

Course

MATH 2.03

Subject

Mathematics

Date

Dec 18, 2024

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Uploaded by UltraMoon8663

How do we Protect Endangered Species? The projected population P of the new colony t days after the transfer is given by !(#) =!"#$%&$#"."(&. 1.What is the projected population of the colony after 1 year? After 2 years? 2.Now let’s see what happens after many, many years have passed. a.Fill in the table for large values of t. #10,000 100,000 500,000 1,000,000 !(#)b.After many, many years, what do you predict will happen to the insect population? 3.Sketch a graph of the population P as a function of time. 4.Explain the meaning of any asymptotes in the context of this problem. 5.As tcontinues to increase, which grows faster: the numerator of !(#)or the denominator? How do you know? 6.How can you tell just by looking at the equation what the population of insects will do in the long run? A rare species of insect was discovered in the Amazon Rainforest. To protect the species, entomologists (scientists who study insects) declared the insect endangered and transferred a population of 30 insects to a protected area. They now want to study this population over time. t days Population P(365)=1625.7P(730)=1968.82451.62495.I24992499.5limp4)""◦°Ithinkthepopulationwillstabilizeat→°2500insects.*wiwn¥%rHorizontalasymptoteaty=zsoomeansthatthepopulationhasacarryingcapacityandwon'tg¥eF%r9exceed-2500insects.behaviorThenumeratorgrowsfaster.Althoughboththenumerator+denominatorarelinear,thenumeratorhasaslopethat's2500timesbiggerthanthedenominator.Ratioof=2500leadingcoefficients

Lesson 8.7 – Limits at Infinity QuickNotes Check Your Understanding Use the graph of !(#)to answer questions 1-3. 1.Evaluate each limit: a.lim!→#!(#)b.lim!→$!!(#)c.lim!→$"!(#)d.lim!→%&!(#)e.lim!→'!!(#)2.List all vertical asymptotes. 3.List all horizontal asymptotes. 4.For which of the following functions is lim!→&!(#) = 0? I.!(#) ='!%()#II. !(#) =*!$+#!%(!%%,!$+-!%.III. !(#) =(!%-)(!+#)(!%()A)I only B) II only C) II and III only D) I and III only E) I, II, and III 5.Write the equation of a function *(#)where lim!→&*(#) =#(and lim!→%'"*(#) = −∞!(#)(EndBehavior)him✗→asf(×)=a㱺horizontalasymptoteaty=aeim✗→bfcx)=as㱺verticalasymptoteat✗=bTOfindendbehaviorcomparenumerator+denominatorDeg.ofnum>Deg.Ofdenom㱺nohorizontalasymptoteDegofnum<Deg.ofdenom㱺It.Aat4=0Degofnum=Degofdenom㱺H.Aaty-Y.ci?-o,YameEhhYn-ator:as:✗=0,✗=34=20¥pmia◦°0a"1%drˢatic⑨y=4€27vA@✗=-3H-Aat51×+3)y=41s