Name:______________________________________________Date:____________________Period:_____
Algebra1
Assignment53:Exponential,Quadratic,andLinearRegression
1. Thetablebelowshowsanexponentialfunctionregardingtheamountofbacteriabythehour.
Whatisthey-intercept?____________
0
Amount
(cm)
0.10
IsthisGrowthorDecay?____________
1
0.15
2
0.2
3
0.3
4
0.4
5
0.6
Equation:________________________________
Isthegraphincreasingordecreasing?_________
Whatis!(3)?___________Whatis!(10)?________
Hour
6
0.8
After13hourshowmuchbacteriaispresent?_________
7
1.15
8
1.5
2. Thetablebelowshowsthelinearrelationshipsbetweentheweightandheightforagroupofcollege
students.
Weight
(lbs)
210
170
220
184
180
245
183
194
190
213
Equation:________________________________
Whatisthey-intercept?____________
Isthegraphincreasingordecreasing?_________
Whatis!(160)?________
Whatis!(180)?___________
Estimatetheheightofapersonwhois240lbs._________
72
65
75
68
66
77
67
71
69
74
3. ApennyisdroppedoffoftheEmpireStateBuilding.Thepenny’squadratic
pathwayismodeledbythetabletotheright.
Equation:________________________________
Seconds
Feet
0
1250
3.5
1054
5
850
Whatdoesthey-interceptrepresent?_____________________
6
674
8.5
94
Whatisthey-intercept?____________
Zeros?__________
Whenwillthepennyhittheground?_____________
Height(in)
After7seconds,whatistheheightofthepenny?____________________
4. Theexponentialtableshowsthevalueofacarduringcertainyears.Writeanequationforthecurveof
bestfit.Thenestimatethevalueofthecarin2016.
Equation:________________________________
Whatdoesthey-interceptrepresent?____________
GrowthorDecay?__________
Whatisthegrowth/decayrate?_____________
Whatisthegrowth/decayfactor?_____________
Year
$
2008
27,500
2009
24,200
2010
21,296
2011
18,740
2012
16,492
Valueofthecarin2016?_______________
5. In1960,Tompurchasedanantiquecarfor$10,000.Theexponentialmodelshowshowthecarhas
changedfrom1950to1980.
Year
Value
1960
10,000
Equation:________________________________
GrowthorDecay?__________
Whatisthegrowth/decayfactor?_____________
Whatisthegrowth/decayrate?_____________
1965
21,000
1970
41,000
1975
82,000
1980
163,000
Howmuchwasthecarworthin1986?______________
6. Thisgraphrepresentsthenumberofdailyvisitors,y,toanewwebsiteafterxdays.
a. Linear,Quadratic,Exponential?
b. Whatistheequationforthegraph?
c. Whatisthey-intercept?
d. Whatdoesthey-interceptrepresent?
e. Isthegraphincreasingordecreasing?Whatdoesthatmean?
NumberofVisitors
f. Whatis!(2)?Whatis!(5)?
g. Approximatehowmanyvisitorstherewillbeaftersixdays?
NumberofDays
7. Theexponentialfunctionbelowrepresentsthevalue
ofamotorcycleafteritwasboughtfromthedealership.
a. GrowthorDecay?Whatistheavalue?
b. Whatistheinitialvalue?
c. Whatisthey-interceptandwhatdoesitmean?
$Value
d. Approx.howoldisthemotorcycle
whenitisworth$6000?
Years
e. Whatistheapprox.valueofthemotorcycleafter11years?
8. Thegraphshowsthefunction! ! = ! ! .
Whichstatementmustbetrueaboutb?
9. Thetableshowsthepopulation,p,ofmiceina
fieldattheendofmmonths.
A. ! > 1
B.0 < ! < 1
C. ! < 0
D.! < −1
Basedonthedatainthetable,whatwillbethe
populationofmiceinthefieldattheendof8
months?
A.192B.3,072
C.1,536D.256
10. Joycewon$400inanessaycontest.Sheinveststhemoneyinaninterestearningaccount.Usingthetable,findthecorrectexponentialmodeland
useittopredictapproximatelywhenJoycewillhave$800intheaccount.
A.!
B.!
C.!
D.!
! = 400(1.06)! ;about12years
! = 1.06 400 ! ;about2years
! = 400(1 + 0.06)! ;about11years ! = 400(0.94)! ;about1.5years
Joyce’s Account
Year
Value
0
$400.00
1
$424.00
2
$449.44
3
$476.41
4
$504.99
5
$535.29