unit 2 review
DESCRIPTION
Unit 2 review. Test tomorrow 3/1/13 15- non-calculator multiple choice 15-Free response questions. Unit 2 test review. 1) y = 3 x 2. y = -2(0.75) x Domain: all real #’sDomain: all real #’s Range: y > 0Range: y < 0. 3) $3745.32 4) $21300 5) a. $16,436.19 - PowerPoint PPT PresentationTRANSCRIPT
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TEST TOMORROW 3 /1 /1315- NON-CALCULATOR MULTIPLE CHOICE
15-FREE RESPONSE QUESTIONS
Unit 2 review
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Unit 2 test review
1) y = 3x 2. y = -2(0.75)x
Domain: all real #’s Domain: all real #’sRange: y > 0 Range: y < 0
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3) $3745.32
4) $21300
5) a. $16,436.19
b.$16,487.21
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6)
7)
8)
9) 3 10) 4 11) 2/3
2100log
3729log9
364log4
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12)
13)
14)
15) 1
24log
7log x
58log
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16) 0.9307 17) -0.4717 18) 2.7925
19) 25 20) 100
21) 4.266… 22)40
23) 4.6931 24) 16.2905
25) 4386.53 26)0.6065
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27) a. 1.6357 7 years ( 1 year & 7 months)
b. 27.62 years
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Unit 2 overview
Logarithm Evaluate, Properties, and solve Natural logs
Exponential Growth and decay graphs Growth and decay word problems (savings)
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Unit 2- exponential functions
Standard Form: y = abx
a = Y - INTERCEPTb = 0 < b < 1, DECAY b > 1, Growth
Sketch a graph of each equation
y = 3xy = 2(0.75)x
Domain: ALL REAL# Range: y > 0
Domain: ALL REAL# Range: y > 0
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Growth or Decay???
y = 8x y = 4 · 9x
y = 0.65x
y = 3 · 1.5x
y = 0.1 · 0.9x
y = 0.7 · 3.3x
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Unit 2- exponential word problems
nt
nrpa )1( rtpeA
tray )1(
Growth/Decay $ compounded Continuously $ compounded n, number of times
14
32.3745$)045.1(1000.3 30 yy
23.736$)1206.1(300.4 )15*12( yy
82.730,24$15000.5 )1005(. yey
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$200 principal, 4% compounded annually for 5 years
$1000 principal, 3.6% compounded monthly for 10 years
$3000 investment, 8% loss each year for 3 years
nt
nrpa )1(
tray )1(
tray )1(
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Find the balance in each account.You deposit $2500 in a savings account with 3% interest
compounded annually. What is the balance in the account after 6 years?
You deposit $750 in an account with 7% interest compounded semiannually. What is the balance in the account after 4 years?
You deposit $520 in an account with 4% interest compounded monthly. What is the balance in the account after 5 years?
tray )1(
nt
nrpa )1(
nt
nrpa )1(
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Unit 2 - LOGARITHMS
Logarithms:logb a = x → bx=a log a = x→ 10x=a ln a = x →
ex=a
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Unit 2 – Solving exponential
Solving Exponential Equations Get the Base & exponent alone. Then write in LOG form, Solve for the
variable13. 16.
25 20x 5 32x
e
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Unit 2 – log properties
Use log properties to combine logs ADD = Multiply, Sub =Divide, # in front goes as ExponentWrite each expression as a single
logarithm.17. log 8 + log 3 18. 3 log x + 4 log x19. log 4 + log 2 log 5
24log7log x
58log
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Unit 2 – solving log equations
Use properties to combine into single logThen write in EXPONENTIAL form, then solve
for the variable.20. log 3x − log 5 = 1
21. 2 log x − log 3 = 1
22. log 8 − log 2x = − 1
23. ln x ln 4 = 7
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Logarithms
Logarithms are used to solve for the exponent. (it gets the exponent alone)
log yxxb by
Write each in log form:1) 100 = 102
2) 34 = 81
Write each in exponential form:
3125log)3 5
61.15ln)4
2100log10
481log3
125 = 53
e1.61 = 5
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Properties of logs
nb
b
b
mnmmn
log Property Power
log Property Quotient
log Property Product
mnnmnm
b
bb
bb
logloglogloglog
xx 3log5log 22 9log6log2 55 Write each as a single log
22 15log x 9log36log 55
936log5 4log5
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Solve
23log6log x
236log x
x210 2
201. x200x
1624 2 xe
5.32 xex25.3ln
626.0x
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EXPONENTIAL
Expo. Growth and decay
tray )1( Ending amount
Initial amount
Rate(decimal)
Time
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Exponential growth/decayIf you invest $1000 in a savings account
that pays 5% annual interest. How much money will you have after six years?
You buy a new computer for $800. it is expected to depreciated 12% each year. How long will it take for the computer to be worth $500?
$1340.10
3.68 years