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Coordinate Algebra: Unit 3

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Modeling Real World Arithmetic and Geometric Sequences Connections Worksheet

Arithmetic sequences have a common _______________________. It is represented by a ___________________ function model.

Real world situations that can be modeled by arithmetic sequences (linear functions) include:

Geometric sequences have a common _______________________. It is represented by an ____________________ function model.

Real world situations that can be modeled by geometric sequences (exponential functions) include:

You Decide! Which type of sequence would we use the model the situation?

1. Your tuition costs go up $2,000 each semester.

2. You get a 10% salary increase each year you work at Wendy’s

3. There are 40 rows in a theater, and each row has 3 fewer chairs than the row before

4. Each of Lebron’s first three contracts gave him double the guaranteed money as the previous contract.

5. You put your money in a savings account that gains 5% interest annually

6. For every day you miss of school, you lose 2 points from your participation grade.

7. Your weekly allowance goes up $0.25 per week

8. Your hourly wage at work increases by $0.05/hr, then by $0.10/hr, then by $0.50/hr, for each of the first three years that you work

9. There are 40 rows in a theater, and each row has 3 fewer chairs than the row before

10. Each of Lebron’s first three contracts gave him double the guaranteed money as the previous contract.

11. You put your money in a savings account that gains 5% interest annually

12. For every extra question you answer on a quiz, you get 3 more points.

Independent Practice

Explain the type of sequence and why. Then write the explicit formula for the sequence.

1. 100, -50, 25, -12.5, …

2. -10, 30, -90, 270 …

3. 100, 104, 106, 108, …

4. 1, 1.5, 2.25, …

For each word problem, determine the type of sequence and then answer the questions that follow.

1. The deer population in an area is increasing. This year, the population was double last year’s population of 325.

a. What type of sequence is being represented? How do you know?

b. What is the current deer population?

c. Assuming that the population increases at the same rate for the next few years, write an explicit formula for the sequence.

d. Find the expected deer population for the fourth year of the sequence.

2. College tuition costs are increasing, and Monique is trying to decide where she’ll be able to get the best education for her money. She could enroll at Spelman, where it will cost her $30,000 in her first year, and then increase each year at a 10% rate. She could also enroll at Clark Atlanta, which will cost her $25,000 in her first year, but then increase each year at a 25% rate.

a. What is the type of sequence is being represented? How do you know?

b. Write an explicit formula for the tution cost at both schools.

c. Which school will cost more in her senior year (4th year)?

3. Chantelle is applying for scholarships for college. Scholarship A offers her $10,000 in her freshman year, and promises an increase of $2,500 each year. Scholarship B offers her $3,000 in her freshman year, and promises to double the scholarship amount each year.

a. Write an explicit formula for each scholarship offer. Do they both represent the same type of sequence? How do you know?

b. Which scholarship will pay Chantelle the most in her senior year (her 4th year)? How do you know?

4. Latrice is trying to decide between two job offers. She knows she wants to be a teacher, but she doesn’t know what age of students she wants to work with. She could be a high-school science teacher, and be offered a salary modeled by the explicit sequence an = 1,000n + 40,000. She could also be a preschool teacher, and be offered a salary modeled by the explicit sequence an = 2,000n + 25,000. While Latrice loves kids, she needs to take care of her own, so her decision will be dependent on which job allows her to make more money.

a. What type of sequences are being represented here?

b. After her 1st year, which job would pay her more?

c. After her 10th year, which job would pay her more?

d. After her 20th year, which job would pay her more?

e. In which year will both jobs pay her the same salary?

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