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Algebra 2 Name______________________________ ALT 09 Assignment 9.2: Graphing Exponential Decay Determine whether each function represents growth or decay. 1. () = & ( ) * 2. () = + , (3 * ) 3. () = & . ) * 4. () = (0.8) * Match the function with its graph. 5. () = & + , ) * 6. () =− & + , ) * 7. () =3 & + , ) * 8. () = + & + , ) * 9. () = −3 & + , ) * 10. () =− + & + , ) * Depreciation: You buy a new computer and accessories for \$1200. The value of the computer decreases by 30% each year. 11. Write an exponential decay model giving the computer’s value V (in dollars) after t years. 12. What is the value of the computer after 4 years?
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### Transcript of Assignment 9.2: Graphing Exponential Decay

A2 9.2Determine whether each function represents growth or decay.
1. () = &' ( ) * 2. () = +
5. () = &+ , ) * 6. () = −&+
' &+ , ) *
Depreciation: You buy a new computer and accessories for \$1200. The value of the computer decreases by 30% each year. 11. Write an exponential decay model giving the computer’s value V (in dollars) after t years. 12. What is the value of the computer after 4 years?
Graph each equation. 13. () = &,
' ) * 14. () = 2 • &+
' ) * + 2
D: R: D: R: 17. () = (0.5)*8+ 18. () = &+
, ) *9,
Algebra 2 Name______________________
Systems Unit Review Graph the system of equations and determine the solution.
1. x + 2y = 7 3x + y = 6 ! " #
2. x − 5y = −5 3x −15y = 9 " # \$
3. x + y = 4 2x − y = 6 " # \$
Use substitution to solve the system of equations. Remember to write the answer as an ordered pair (x, y).
4. 6x −3y =12 −2x + y = −4 " # \$
5. x + 2y =11 4x +3y = 9 ! " #
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
y = x 1
10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
( 0.5x 0.3y = 1.3
1.4x+ 1.2y = 2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
y = x 1
10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
( 0.5x 0.3y = 1.3
1.4x+ 1.2y = 2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
y = x 1
10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
( 0.5x 0.3y = 1.3
1.4x+ 1.2y = 2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name______________________
Systems Unit Review Graph the system of equations and determine the solution.
1. x + 2y = 7 3x + y = 6 ! " #
2. x − 5y = −5 3x −15y = 9 " # \$
3. x + y = 4 2x − y = 6 " # \$
Use substitution to solve the system of equations. Remember to write the answer as an ordered pair (x, y).
4. 6x −3y =12 −2x + y = −4 " # \$
5. x + 2y =11 4x +3y = 9 ! " #
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
y = x 1
10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
( 0.5x 0.3y = 1.3
1.4x+ 1.2y = 2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
y = x 1
10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
( 0.5x 0.3y = 1.3
1.4x+ 1.2y = 2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
y = x 1
10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
( 0.5x 0.3y = 1.3
1.4x+ 1.2y = 2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name______________________
Systems Unit Review Graph the system of equations and determine the solution.
1. x + 2y = 7 3x + y = 6 ! " #
2. x − 5y = −5 3x −15y = 9 " # \$
3. x + y = 4 2x − y = 6 " # \$
Use substitution to solve the system of equations. Remember to write the answer as an ordered pair (x, y).
4. 6x −3y =12 −2x + y = −4 " # \$
5. x + 2y =11 4x +3y = 9 ! " #
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
y = x 1
10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
( 0.5x 0.3y = 1.3
1.4x+ 1.2y = 2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
y = x 1
10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
( 0.5x 0.3y = 1.3
1.4x+ 1.2y = 2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
y = x 1
10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
( 0.5x 0.3y = 1.3
1.4x+ 1.2y = 2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name______________________
Systems Unit Review Graph the system of equations and determine the solution.
1. x + 2y = 7 3x + y = 6 ! " #
2. x − 5y = −5 3x −15y = 9 " # \$
3. x + y = 4 2x − y = 6 " # \$
Use substitution to solve the system of equations. Remember to write the answer as an ordered pair (x, y).
4. 6x −3y =12 −2x + y = −4 " # \$
5. x + 2y =11 4x +3y = 9 ! " #
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
y = x 1
10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
( 0.5x 0.3y = 1.3
1.4x+ 1.2y = 2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
y = x 1
10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
( 0.5x 0.3y = 1.3
1.4x+ 1.2y = 2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
y = x 1
10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
( 0.5x 0.3y = 1.3
1.4x+ 1.2y = 2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name______________________
Systems Unit Review Graph the system of equations and determine the solution.
1. x + 2y = 7 3x + y = 6 ! " #
2. x − 5y = −5 3x −15y = 9 " # \$
3. x + y = 4 2x − y = 6 " # \$
Use substitution to solve the system of equations. Remember to write the answer as an ordered pair (x, y).
4. 6x −3y =12 −2x + y = −4 " # \$
5. x + 2y =11 4x +3y = 9 ! " #
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
y = x 1
10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
( 0.5x 0.3y = 1.3
1.4x+ 1.2y = 2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
y = x 1
10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
( 0.5x 0.3y = 1.3
1.4x+ 1.2y = 2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
y = x 1
10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
( 0.5x 0.3y = 1.3
1.4x+ 1.2y = 2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name______________________
Systems Unit Review Graph the system of equations and determine the solution.
1. x + 2y = 7 3x + y = 6 ! " #
2. x − 5y = −5 3x −15y = 9 " # \$
3. x + y = 4 2x − y = 6 " # \$
Use substitution to solve the system of equations. Remember to write the answer as an ordered pair (x, y).
4. 6x −3y =12 −2x + y = −4 " # \$
5. x + 2y =11 4x +3y = 9 ! " #
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
y = x 1
10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
( 0.5x 0.3y = 1.3
1.4x+ 1.2y = 2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
y = x 1
10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
( 0.5x 0.3y = 1.3
1.4x+ 1.2y = 2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3
Algebra 2 Name:
Chapter 3 Review – Systems of Equations and Matrices
For exercises 1-3, graph the system of equations and determine the solution.
1.
y = x 1
10
10
For exercises 4-7, use substitution to solve the system of equations.
4.
( 0.5x 0.3y = 1.3
1.4x+ 1.2y = 2.2
For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.
8.
12. Write a system of equations that has no solutions.
13. Write a system of equations that has infinitely many solutions.
14. Write a system of equations that has exactly one solution.
15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice
exercises worth 4 points each and the free response exercises worth 6 points each.
(a) Let m represent the number of multiple choice exercises and f represent the number of free response
exercises. Write a system of two equations to represent the situation.
(b) Solve your system of equations to part (a).
1 of 3