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Unit 2 review

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 #’s Domain: all real #’s Range: y > 0 Range: y < 0 . 3) $3745.32 4) $21300 5) a. $16,436.19

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Unit 2 review

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  1. Unit 2 review Test tomorrow 3/1/13 15- non-calculator multiple choice 15-Free response questions

  2. Unit 2 test review 1) y = 3x 2. y = -2(0.75)x Domain: all real #’s Domain: all real #’s Range: y > 0 Range: y < 0

  3. 3) $3745.32 4) $21300 5) a. $16,436.19 b.$16,487.21

  4. 6) 7) 8) 9) 3 10) 4 11) 2/3

  5. 12) 13) 14) 15) 1

  6. 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

  7. 27) a. 1.6357 7 years ( 1 year & 7 months) b. 27.62 years

  8. Unit 2 overview • Logarithm • Evaluate, Properties, and solve • Natural logs • Exponential • Growth and decay graphs • Growth and decay word problems (savings)

  9. Unit 2- exponential functions Standard Form: y = abx a = Y - INTERCEPT b = 0 < b < 1, DECAY b > 1, Growth Sketch a graph of each equation y = 2(0.75)x y = 3x Domain: ALL REAL# Range: y > 0 Domain: ALL REAL# Range: y > 0

  10. 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

  11. Unit 2- exponential word problems Growth/Decay $ compounded Continuously $ compounded n, number of times

  12. $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

  13. 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?

  14. Unit 2 - LOGARITHMS Logarithms: logb a = x → bx=a log a = x→ 10x=a ln a = x → ex=a

  15. Unit 2 – Solving exponential Solving Exponential Equations Get the Base & exponent alone. Then write in LOG form, Solve for the variable 13. 16.

  16. Unit 2 – log properties Use log properties to combine logs ADD = Multiply, Sub =Divide, # in front goes as Exponent Write each expression as a single logarithm. 17. log 8 + log 3 18. 3 log x + 4 log x 19. log 4 + log 2 log 5

  17. Unit 2 – solving log equations Use properties to combine into single log Then 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

  18. Logarithms Logarithms are used to solve for the exponent. (it gets the exponent alone) Write each in log form: Write each in exponential form: 1) 100 = 102 125 = 53 2) 34 = 81 e1.61 = 5

  19. Properties of logs Write each as a single log

  20. Solve

  21. EXPONENTIAL Expo. Growth and decay Time Ending amount Rate(decimal) Initial amount

  22. Exponential growth/decay If you invest $1000 in a savings account that pays 5% annual interest. How much money will you have after six years? $1340.10 • 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? 3.68 years

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