2. Algebra 3-4 Chapter 10 Review Algebra 3-4 Chapter 10 Review Sports Challenge! G. Anthony Streamwood High School ©2006 Any changes to the program is a copyright violation. G. Anthony Streamwood High School ©2006 Any changes to the program is a copyright violation.

3. HOME VISITOR GAME BOARD GAME BOARD GAME BOARD GAME BOARDEquations/FormEvaluate/SolveSolveExpress/SolveSolve 100 200 300 400 500 Let’s Play FINAL CHALLENGE FINAL CHALLENGE

4. HOME VISITOR GAME BOARD GAME BOARD GAME BOARD GAME BOARD Solve 7 10n-14 = 7 -4 100 7 10n – 14 = 7 -4 10n – 14 = -4 10n = 10 n = 1 Equations/Form for 100

5. HOME VISITOR GAME BOARD GAME BOARD GAME BOARD GAME BOARD Solve 5 5n + 5 = 625 200 5 5n + 5 = 5 4 5n + 5 = 4 5n = -1 n = -1/5 Equations/Form for 200

6. HOME VISITOR GAME BOARD GAME BOARD GAME BOARD GAME BOARD log b x = n means b n = x Write in log form: 9 2 = 81 300 log 9 81 = 2 Equations/Form for 300

7. HOME VISITOR GAME BOARD GAME BOARD GAME BOARD GAME BOARD log b x = n means b n = x Write in exponential form: log 2 (1/8) = -3 400 2 -3 = 1/8 Equations/Form 400

8. HOME VISITOR GAME BOARD GAME BOARD GAME BOARD GAME BOARD log b x = n means b n = x Write in exponential form: log 2 (1/32) = -5 500 2 -5 = 1/32 Equations/Form for 500

9. HOME VISITOR GAME BOARD GAME BOARD GAME BOARD GAME BOARD Evaluate log 4 256 100 256= (4)(4)(4)(4)= 4 4 log 4 4 4 = 4 Evaluate/Solve for 100

10. HOME VISITOR GAME BOARD GAME BOARD GAME BOARD GAME BOARD Evaluate log 9 1/729 200 1/729 = 9 -3 log 9 9 -3 = -3 Evaluate/Solve for 200

11. HOME VISITOR GAME BOARD GAME BOARD GAME BOARD GAME BOARD Solve log 32 n = 4/5 300 log 32 n = 4/5 n = 32 4/5 n = 2 5(4/5) n = 2 4 = 16 Evaluate/Solve for 300

12. HOME VISITOR GAME BOARD GAME BOARD GAME BOARD GAME BOARD Solve log 2 x = 6 400 log b x = n means b n = x log 2 x = 6 x = 2 6 x = 64 Evaluate/Solve for 400

13. HOME VISITOR GAME BOARD GAME BOARD GAME BOARD GAME BOARD Use log 2 3 ≈ 1.5850 and log 2 2 ≈ 1 to approximate log 2 288 500 288 = 2·2·2·2·2·3·3 log 2 288 = log 2 (2 5 ·3 2 ) 5(1) + 2(1.585) = 8.17 Evaluate/Solve for 500

14. HOME VISITOR GAME BOARD GAME BOARD GAME BOARD GAME BOARD Use a calculator to find Log 4 1536 100 log 4 1536 = log 1536/log 4 =5.2925 Solve for 100

15. HOME VISITOR GAME BOARD GAME BOARD GAME BOARD GAME BOARD Solve log 2 7 + log 2 a = log 2 18 200 log 2 (7a) = log 2 18 7a = 18 a = 18/7 Solve for 200

16. HOME VISITOR GAME BOARD GAME BOARD GAME BOARD GAME BOARD Solve log 5 (x + 2) – log 5 = log 5 64 300 log 5 (x + 2)/8 = log 5 64 (x + 2)/ 8 = 64 x + 2 = 512 x = 510 Solve for 300

17. HOME VISITOR GAME BOARD GAME BOARD GAME BOARD GAME BOARD Solve 3 8x = 18 400 log 3 8x = log 18 8x log 3 = log 18 8x = log 18/log 3 8x = 2.6309 x =.3289 Solve for 400

18. HOME VISITOR GAME BOARD GAME BOARD GAME BOARD GAME BOARD Solve 9 4a < 29 500 log 9 4a < log 29 4a log 9 < log 29 4a < log 29/ log 9 4a < 1.5325 a <.3831 Solve for 500

19. HOME VISITOR GAME BOARD GAME BOARD GAME BOARD GAME BOARD Express the given log in terms of a common log. Approximate its value to four decimal places: log 7 5.2 100 log 7 5.2 = log 5.2/log 7 log 7 5.2 =.8472 Express/Solve for 100

20. HOME VISITOR GAME BOARD GAME BOARD GAME BOARD GAME BOARD Express the given log in terms of a common log. Approximate its value to four decimal places: log 3 19 200 log 3 19 = log 19/log 3 log 3 19 = 2.6801 Express/Solve for 200

21. HOME VISITOR GAME BOARD GAME BOARD GAME BOARD GAME BOARD Evaluate the expression ln e 2 300 log e n = n ln e 2 = 2 Express/Solve for 300

22. HOME VISITOR GAME BOARD GAME BOARD GAME BOARD GAME BOARD Solve 6e x – 4 = 7 400 6e x – 4 = 7 6e x = 11 e x = 11/6 ln e x = ln 11/6 x =.61 Express/Solve for 400

23. HOME VISITOR GAME BOARD GAME BOARD GAME BOARD GAME BOARD Solve 4 + 2e 6x = 29 500 4 + 2e 6x = 29 2e 6x = 25 e 6x = 25/2 ln e 6x = ln (25/2) 6x = 2.527 x =.4210 Express/Solve for 500

24. HOME VISITOR GAME BOARD GAME BOARD GAME BOARD GAME BOARD Solve e x > 16 100 e x > 16 ln e x > ln 16 x > 2.7726 Solve for 100

25. HOME VISITOR GAME BOARD GAME BOARD GAME BOARD GAME BOARD Pappa Industries bought a specialized digital scanner for $800. It is expected to depreciate at a rate of 10% per year. What will the value of the scanner be in 2 years? 200 decay y = a(1 – r) t a = initial amount t = time y = 800(1 -.10) 2 y = 800(.81) y = 648 The value will be $648 in 2 years. Solve for 200

26. HOME VISITOR GAME BOARD GAME BOARD GAME BOARD GAME BOARD Huro Retail Stores bought a touch screen monitor for $1200. It is expected to depreciate at a rate of 25% per year. What will the value of the monitor be in 3 years? 300 y = 1200(1 –.25) 3 y = 1200(.4219) y = 506.25 The monitor will be worth $506.25. Solve for 300

27. HOME VISITOR GAME BOARD GAME BOARD GAME BOARD GAME BOARD Mike invests $1000 in a savings bond that pays 5% interest compounded continuously. What will be the values in 3 years? 400 y = ae kt y = 1000e.05(3) y = 1161.83 The bond will be worth $1161.83 in three years. Solve for 400

28. HOME VISITOR GAME BOARD GAME BOARD GAME BOARD GAME BOARD Arturo’s stock investments have been increasing 7.8% per year. He initially started with $750. How much will his stocks be worth in three years? 500 growth y = a(1 + r) t y = 750(1 +.078) 3 y = 750(1.2527) y = $939.55 Solve for 500

29. HOME VISITOR GAME BOARD GAME BOARD GAME BOARD GAME BOARD Write Your Final Challenge Wager Sue invests $1000 at 5% interest compounded continuously and Norma invests $1250 at 3.5% interest compounded continuously. When interest is compounded continuously, the amount A in an account after t years is found using the formula A = Pe rt, where P is the amount of principal and r is the annual interest rate. In how many years will Sue’s account be greater than Norma’s account? Final Challenge 00:00:0000:00:0100:00:0200:00:0300:00:0400:00:0500:00:0600:00:0700:00:0800:00:0900:00:1000:00:1100:00:1200:00:1300:00:1400:00:1500:00:1600:00:1700:00:1800:00:1900:00:2000:00:2100:00:2200:00:2300:00:2400:00:2500:00:2600:00:2700:00:2800:00:2900:00:30 END GAME END GAME END GAME END GAME 1000e 0.05t > 1250e 0.035t ln 1000e 0.05t > ln 1250e 0.035t ln 1000 + ln e 0.05t > ln 1250 + ln e 0.035t ln 1000 + 0.05t > ln 1250 + 0.035t ln 1000 + 0.015t > ln 1250 0.015t > ln 1250 – ln 1000 t >(ln 1250 – ln 1000)/0.015 t ≥ 14.88 After about 15 years, Sue’s account will be greater than Norma’s account.

30. GoodBye GAME OVER

31. Double Score DOUBLE SCORE!