assignment 47 solving log equations - lehi...

ALGEBRA 2 ~ Lessons 47 – 59 Remember to write the original problem and show all of your

steps! All work should be done on a separate piece of paper.

Assignment 47 – Solving log equations

New: Solve.

1. 2. 3. 4. 5. 6. 7. 2 8. 9. 10. 11.

12. 13.

14. 15.

Review (No Calculators):

16. Solve by quadratic formula: 11 17. Put the following in vertex form, then name the vertex and direction of opening

of the graph: f(x) = 3 18. Find the inverse of the relation and determine whether the inverse is a function: {(3, 7), (1, 4), (-2, 7), (0, 3)}

19. Determine whether the pair of functions are inverses: f(x) = , g(x) = 5x - 1

(Continued on next page…)

Draw the graph of the following functions and list the horizontal asymptote. Label 2 points on each graph.

20. g(x) = 21. y = 22. y = Evaluate:

23. 24.

Draw the graph of the following functions and list the vertical asymptote. Label 2 points on each graph. 25. g(x) = 26. Use log rules to expand the expressions.

27. 28.

Write the expressions as the log of a single quantity. 29. 30. 3 Solve.

31. 32.

Use Calculator

33. Find the vertex of the parabola: f(x) = 34. Solve: x – y + 3 = 0

y = 35. Write an equation for each situation and solve. Round to 2 decimals. You need to barrow $2500 for a car. You plan to pay it back all at once in 5 years at 3.5% interest a year. How much will you have to pay?

36. Evaluate to 3 decimals. You must show a step: Solve. Give the exact answer and the answer to 3 decimals.

37. 38. 39.

Assignment 48 – Growth and Decay problems

New: Give the percent growth or decay represented by the following equations.

1. = 11 2. = 15 3. = 45 4. = 3

Write an equation for the following situations and solve. Round final answers to 2 decimals. 5. Derek invested $1500 into an account that pays 9% interest. How long must the money be left in the account for it to grow to $2150? 6. How many years will it take a sum of money to double if it is invested at 15% 7. At what annual rate will $1000 have to be invested to amount to $2500 in 10 years? 8. You want $500 to grow to $1000 in 7 years. What interest rate will you need to get? 9. If the world population is about 6 billion people now, and if the population grows continuously at an annual rate of 1.7%, a. what will the population be in 10 years? b. How long will it take to reach 9 billion people? 10. The Sawyers bought a condominium for $75,000. Assuming that its value will appreciate 6% a year, a. how much will the condo be worth in five years? b. How long until the condo is worth $125,000 11. Element X has a half-life of 2000 years. Starting with 830 grams, a. how many grams will be left in 105 years? b. how long until 200 grams remain? 12. The half-life of element Y is 57 minutes. Starting with 35 milligrams, a. how many milligrams will be left after 1.5 hours? b. how long will it take to decay to 5 mg?

Review (No Calculator):

13. Express in simplest radical form:

14. Solve:

15. Solve by graphing: y > | x – 2 | - 4

y <


16. Graph, label 2 points and give the horizontal asymptote: y =

17. Write the log equation in exponential form:

18. Write the exponential equation in log form:

Evaluate.

19. 20.

Use log rules to expand the expressions

21. 22.

23. Write the expression as the log of a single quantity: Solve.

24. 25.

26. 27. 3 28.

29. 30.

Use Calculator:

31. Solve by graphing: 32. Write an equation for the situation and solve. Round to 2 decimals.

Chuck’s dad puts $2000 in a college fund on his 12th birthday. The account pays 5% interest. How much does Chuck have in the account when he turns 18?


34. 35. 36.

Assignment 49 – Right triangle trig (13-1)

New: Book: Pg. 777 #9 – 15 odd, 23 – 37 odd, 41, 43 For each function, find the exact value of the other 2 trig functions (

1. 2. 3.

Review (No Calculator):

4. Simplify:

5. Graph, label 2 points and give the horizontal asymptote:

6. Evaluate:

7. Draw the graph of the following functions and list the vertical asymptote. Label 2 points on each graph:

8. Use log rules to expand the expressions:

Write the expression as the log of a single quantity:

9. 10.

Solve:

11. 12. 13.

14. 15. 16. Give the percent growth or decay represented by the following equations. 17. 11 18. 15 (Continued on the next page…)

Use Calculator

19. Solve – round to 3 decimals: 20. Write an equation for the situation and solve. Round to 2 decimals.

You want to go on a cruise that cost $3500 in 6 years. How much should you deposit in the bank now, at 8%, so that you will have enough to go?


22. 23. 24. Write an equation for the following situations and solve. Round final answers to 2 decimals. 25. Lisa invested $6500 into an account that pays 6% interest. How long must the money be left in the account for it to grow to $8000? 26. If a city population is about 112,000 people now and if the population grows continuously at an annual rate of 4%, a. what will the population be in 7 years? b. How long will it take to reach 250,000 people?

Assignment 50 – Degrees, radians, co-terminal

angles (13-2)

New: Book: Pg. 783 #7 – 17 odd, 21 – 45 odd

Test Review 12 ~ Complete blue packet

TEST 12

Assignment 51 – Unit circle

New: COMPLETE THE UNIT CIRCLE MONSTER! Check it with the teacher.

You may use this circle to help you complete your assignment:

Find in radians (you may have more than 1 answer)

1. 2. 3.

4. 5.

Find in degrees (you may have more than 1 answer)

6. 7. 8.

9. 10.

Find in radians on your calculator. Round to 4 decimals

11. 12. 13.

Review (No calculator): 14. Factor: 5xy – 3y + 10x - 6 (Continued on next page…)

15. Simplify:

16. Find the inverse: f(x) = 17. Write the expression as the log of a single quantity: Solve:

18. 19. 20. 21.

22. Find the exact value of the other 2 trig functions:

Use a calculator


24. 25. 500 Write an equation for the following situations and solve. Round to 2 decimals. 26. How many years will it take a sum of money to double if it is invested at 7% interest? 27. At what annual rate will a sum of money triple in 12 years? 28. Radium has a half-life of 1620 years. A 20 gram sample is sealed in a box. a. How many grams will be left in 5000 years? b. How long until 5 grams remain? AND Book: (calculator) Pg. 777 #8 – 14 even (no calculator) Pg. 784 #16 – 22 even, 34

Assignment 52 – Arc length and area of a sector

New: Find the length of each arc:

1. 2. 3.

4. radius = 8 in. 5. Radius = 27 yds. 6. Radius = 6 m

Given the radius of a circle and an arc length, find the central angle, . 7. radius = 2 in. 8. radius = 7 ft. 9. radius = 24 ft. arc length = 8 in. arc length = 4 ft. arc length = 16 ft. Find the area of each shaded sector of a circle. 10. 11. 12.


Find the area of each shaded sector of a circle. 13. 14. 15.

16.

Review (No calculator): 17. Solve: | x + 14 | + 3 > 17

18. f(x) = , h(x) = x – 1 Find: Solve:

19. 20. 21. 22.


Find in radians (you may have more than 1 answer) (use circle from assign. 51)

24. 25.

Find in degrees (you may have more than 1 answer).

26. 27.


Use Calculator

28. Find the zeros – round to 3 decimals: f(x) = 15.4 Write an equation for the following situations and solve. Round to 2 decimals. 29. You want $750 to double in 5 years. What interest rate will you need to get? 30. How many years will it take a sum of money to double in it is invested at 3.5%? 31. It is estimated that there are 4100 rabbits on an island, with a growth rate of 55% a year. a. How many rabbits will be on the island in 3 years? (whole number) b. How long until there are 50,000 rabbits?

32. Find in radians. Round to 4 decimals: AND Book: (calculator) Pg. 778 #22, 34, 38 (no calculator) Pg. 784 #24, 26, 30, 32, 44

Assignment 53 – Graphing trig functions

New: State the amplitude and period of each function:

1 2 2. 3. 3

4. 5 5. 6

State the amplitude and period of each function, then draw the graph. You must label 4 angles on the x-axis

6. 3 7. 8. 4

9. 10. 2

Review:

11. Solve:

12. Solve by quadratic formula: 4 (Continued on next page…)

Solve:

13. 14.

Evaluate (you can use the circle from assignment 51).

15. cos 16. 17.

18. 19. Find the length of each arc (use the circle below for both 20 and 21).

20. 21.

22. Given the radius = 15 in. and an arc length of 4 in. Find the central angle, Find the area of each sector of a circle. 23. radius = 4 cm 24. Radius = 7 km

Use Calculator

25. Solve. Give the exact answer and the answer to 3 decimals: 1000 26. Write an equation for the following situations and solve. Round to 2 decimals. The half-life of element X is 32 years. Starting with 25 grams: a. How many grams will be left after 10 years? b. How long will it take to decay to 10 grams? AND Book: (calculator) Pg. 778 #24, 28, 36, 52 (no calculator) Pg. 784 #28, 36, 38, 46

Assignment 54 – Counting (12-1, 12-2)

New: Book: Pg. 715 #3, 11, 23, 27, 29, 31, 33 Pg. 723 #11, 15 – 25 odd, 33, 41, 43 (no calculator #33)

Test 13 Review ~ Complete Blue Worksheet

Test 13

Assignment 55 – Combinations (12-3)

New: Book: Pg. 729 #7 – 37 odd, 41, 43(skip d), 45 (no calculator on #9, 23, 25)

Review:

1. Solve: –

2. Solve by substitution or elimination:

3. Find


5. Change 255 to radians

6. Change -4 to degrees (Continued on next page…)

Use the circle on Assignment 51 to help you with #7-10. Evaluate.

7. 8.

9. Find in radians if tan

10. Find in degrees if sin

11. Find the length of the arc

12. Find the length of an arc if the radius is 40 cm and =

13. Find the central angle, if the radius of a circle is 35 ft. and an arc length is 14 ft. 14. Find the area of the shaded sector

15. State the amplitude and period of the function y =


16. y = 17. y =


May use calculator

18. Solve the right triangle. Angle C is . Round the sides to the nearest tenth and the angle to the nearest degree.

B = 45 , c = 12 AND Book: (use calculator) Pg. 716 #22, 24 Pg. 723 #13c, 18, 22

Assignment 56 – Probability part 1 (12-4, 12-5)

New: Book: (calculator when needed) Pg. 735 #13, 15, 31 – 37 odd Pg. 742 #7 – 13 odd, 17, 21, 25, 27, 29

Review:

1. Simplify:

2. Express in simplest radical form:

3. Simplify:

Find one positive and one negative angle that are coterminal with each angle

4. 125 5.

Evaluate. Use the circle on journal 51 to help you

6. 7.

8. Find the length of the arc


9. Find the central angle, if the radius of a circle is 16 ft. and an arc length is 10 ft. Find the area of the sector of a circle, given: 10. radius = 12 cm 11. Radius = 6 km


12. 13.

AND Book: Pg. 723 #20, 24, 30, 32, 34 (no calculator 32,34) Pg. 729 #6, 10, 14, 20, 34 (no calculator 10)

Assignment 57 – Probability part 2 (12-6)

New: Book: (calculators when needed) Pg. 748 #5 – 13 odd, 14 – 17, 19, 23

Review:

1. Use log rules to expand the expressions:

2. Find in radians if sin

3. Find in degrees if tan

4. Find the length of an arc if the radius is 24 cm and =

5. Find the area of the shaded sector



6. 7.

May use calculator 8. Define 2 variables, write equations, solve by any method, and label your answers correctly Jonah sells popcorn and peanuts at a game. Each bag of popcorn costs $1.50, and a bag of peanuts is $2.25. One night he sold 300 items and made $622.50. How many of each did he sell? 9. Write an equation for the situation and solve. Round to 2 decimals.

If you put $3000 in the bank at 5% interest, how much would you have in 25 years?

AND Book: (calculator when needed) Pg. 715 #10, 26, 32 Pg, 729 #8, 36, 40, 42, 44 Pg. 736 #30, 32, 50 Pg. 742 #8, 10, 12

Assignment 58 – Statistics

New: Book: Pg. 240 #7, 9, 17 Pg. 389 #11, 17, 19 Use this histogram to answer #1 and 2

1. In which interval is the 25th percentile located? 2. In which interval is the 75th percentile located? (Continued on next page…)

Use this histogram to answer #3, 4

3. In which interval is the 30th percentile located? 4. In which interval is the 67th percentile located? Look at the stem and leaf plot on page 389, #15 5. The number 45 is at what % 6. The number 68 is at what % Look at the stem and leaf plot on page 389, #17 7. The number 3.8 is at what % 8. The number 4.3 is at what %

Review (No Calculator): 9. Find the inverse: f(x) = 10. Find one positive and one negative angle that are coterminal with each angle:

11. Find in radians. (may use circle on journal 51 to help): cos

12. Find the length of an arc if the radius is 15 yds. and =

13. Find the area of the sector of a circle if the radius = 6 in. and the central angle

is


14. 15.

(Continued on next page….)

AND Book: Pg. 923 #1, 2, 5 – 8 (no calculator #1, 2) Pg. 729 #22, 38 Pg. 736 #34, 36, 38 Pg. 743 #20, 22 Pg. 748 #8, 10, 12, 18, 22

Test Review 14 ~ Complete blue worksheet

Test 14

ASSIGNMENT ANSWERS: Assignment 47 answers:

1. x = 5 2. x = 6 3. x = 4. x =

5. x = 6. y = 13 7. x = 3, 6 8. x = 6

9. x = 10. x = 4 11. x = 1, 12. x =

13. x = 18 14. x = 3, -3 15. x= 3 16.

17. Vertex: (-3/2, 5/4 ), opens up,

18. {(7, 3), (4, 1), (7, -2), (3, 0)} Not a function 19. Not inverses

#20-22 and 25-26, check graphs with teacher. 20. HA: y=3 Special points: (0,2), (1, -1)

21. HA: y=2, (2, 3), (3, 5) 22. HA: y=1, (0,2), (-1, 3.7) 23. x=2

24. x=-1 25. VA: x=1, (2, 0), (4, -1) 26. VA: x=-2, (-1, -4), (.7, -3)

27. 28. 29.

30. 31. 32. 33. (-3, 36) 34. (1,4), (4,7)

35. $2,776.78 36. 2.277 37. 38.

39.

Assignment 48 answers: 1. grows by 13% 2. decays by 27% 3. grows by 50%

4. decays by 25% 5. 4 years 6. 4.62 years

7. 9.16% 8. 9.9% 9a. 7.11 billion people

9b. 23.85 years 10a. $101,239.41 10b. 8.51 years

11a. 800.34 g 11b. 4106.22 years 12a. 11.72 mg

12b. 160.02 minutes 13. 14. x=1

15. Check graph with teacher 16. HA: y=1 (2, 0), (3, -2) Check graph with teacher.

17. 18. 19. 2 20. -2

21. 22. 23. 24.

25. 26. 27. 28. 29.

30. 31. 32. 33. 1.975

34. 35. 36.

Assignment 49 answers:

1. 2. 3.

4. 5. HA: , (0, -1), (-1, .7) Check graph with teacher 6. -2

7. VA: x=1, (2, -4), (3,-5), check graph with teacher 8.

9. 10. 11. 12.

13. 14. 15. 16.

17. 21% growth 18. 33% decay 19.

20. $2165.74 21. 1.968 22.

23. 24. 25. 3.46 years

26a) 148,191 people 26b) 20.07 years

Assignment 50 answers: Check back of book.


1. 2. 3. 4.

5. 6. 7.

8. 9. 10.

11. 12. 13.

14. 15. 16.

17. 18. 19. 20.

21. 22. 23.

24. 25. 26. 9.90 years

27. 9.16% 28a) 2.35 g 28b) 3,240 years

Page 777: 8. 10.

12.

14.

Page 784: 16. 18. 20. –

22. 34.


1. 2. 3. 4.

5. 6. 12 m 7. 8.

9. 10. 11. 12.

13. 4 14. 15. 16.

17. 18. 19.

20. 21. 22. 23.

24. 25. 26. 27.

28. 29. 13.86% 30. 19.80 years

31a) 21,349 rabbits 31b) 4.55 years 32. .7227

Page 778: 22.

34.

38.

Page 784: 24. 26. 30. 32. 44.


1. amp. 2, period 2 2. amp. 1, period 3. amp. 3, period 4

4. amp. 5, period 10 5. amp. 6, period 3

6. amp. 3, period 2 7. amp. 1, period

8. amp. 4, period 4 9. Amp. period

10. amp. 2, period

11. 12. 13. 14.

15. 16. 17. 18. 1

19. 20. 21. 22.

23. 24. 25.

26a) 20.13 g 26b) 42.30 years

Page 778: 24. 7.5 28.

36. 52.

Page 784: 28. 36. 38.

46.

Assignment 54 answers: Check back of book Assignment 55 answers: Packet (review): 1. 2. (4, 9) 3.

4. 5. 6.

7. 8. 9. 10.

11. 12. 13. 0.4 14.

15. period = , amp= 5 16. Period = , amp= , check graph with teacher

17. period = , amp = 3, check graph with teacher

18.

Page 716: 22. 40,320 orders 24. 14,601,600 license plates

Page 723: 13c) 6,497,400 ways 18. 120 22. 34,650


Packet (review): 1. 2. 3.

4. 5. 6. 7.

8. 9. 10. 11.

#12 and 13: check graph with teacher 12. period = , amp= 5

13. period = , amp= 2

Page 723: 20. 6 24. 90,720 30. 5040 32. 6 34. 9

Page 729: 6. Permutation 10. 21 14. 924 teams 20. Combination

34a) 84 triangles 34b) 9 octagons 34c) 126 pentagons

34d) 126 quadrilaterals 34e) not possible 34f) 84 hexagons


Page 748: 14. 16.

Packet (review): 1. 2. 3.

4. 5. #6 and 7: Check graphs with teacher

6. period = , amp = 3 7. Period = 7, amp =

8. They sold 370 bags of popcorn and 230 bags of peanuts. 9. $10,471.03

10. 720 schedules 26. 640 possibilities 32. 1344 numbers

Page 729: 8. Combination 36. n=3 40. 129,360 groups

42. 45 44. 7,059,052 combinations

Page 736: 30. 10.91% 32. 50. 120 ways

Page 742: 8. independent 10. 12.

Assignment 58 answers: 1. -50 to -36 2. -35 to -19 3. 74 – 77 4. 82 – 85

5. 12% 6. 82% 7. 50% 8. 70%

9. 10. 11. 12.

13. #14 and 15, check graphs with teacher

14. period = amp= 2 15. Period = , amp =

Page 923: 1. 210 2. 35 5. 362,880 ways 6. 2079 outfits

7. 9,979,200 ways 8. 31,824 teams

Page 729: 22. Combination 38. n=9

Page 736: 34. 36. 38. 0

Page 748: 8. 10.

12. 18.

22.

assignment 47 solving log equations - lehi...

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