TEST TOMORROW 3 /1 /1315- NON-CALCULATOR MULTIPLE CHOICE

15-FREE RESPONSE QUESTIONS

Unit 2 review

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

3) $3745.32

4) $21300

5) a. $16,436.19

b.$16,487.21

6)

7)

8)

9) 3 10) 4 11) 2/3

2100log

3729log9

364log4

12)

13)

14)

15) 1

24log

7log x

58log

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

27) a. 1.6357 7 years ( 1 year & 7 months)

b. 27.62 years

Unit 2 overview

Logarithm Evaluate, Properties, and solve Natural logs

Exponential Growth and decay graphs Growth and decay word problems (savings)

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

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

Unit 2- exponential word problems

nt

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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

$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(

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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(

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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

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

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

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

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

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

Solve

23log6log x

236log x

x210 2

201. x200x

1624 2 xe

5.32 xex25.3ln

626.0x

EXPONENTIAL

Expo. Growth and decay

tray )1( Ending amount

Initial amount

Rate(decimal)

Time

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