URGENT!
An employer provides two payment options for employees.

Option A: Receive $200 the first week. Receive an additional $50 for each of the following weeks.

Option B: Receive $200 the first week. Receive an additional 10% for each of the following weeks.

Complete the tables to show how much money would be received for both payment options, each week, for 6

weeks.

Option A: Week 1 2 3 4 5 6

Amount paid 200 250 300 350 400 450

Option B: 1 2 3 4 5 6

200 220 242 266.20 292.82 322.10

I know the answer to this part but I need help with the rest.

2. Referring to the tables in #1, suppose you are a new employee. You notice that each payment option describes a sequence and decide to use rules to help determine which option to take.

(a) Determine the rule (or formula) for each sequence. Show your work.

(b) Your friend trusts your tables in #1, but wonders if you wrote the rules correctly.

Show two calculations using week 6 to convince your friend that both your rules work.

3. Consider the formulas you wrote in Problem 2.

(a) Your friend says that because the rules are functions, they can be graphed and must have y-intercepts. Do you agree or disagree with your friend? Explain your thinking.

(b) Your friend uses your rules to determine the outputs when the inputs are 18.5.

Explain why she cannot use 18.5, and describe types for numbers that CAN be used for inputs?

4. Use your formulas from #2 to calculate how much each option makes during week 20. (Show your work)

(1) The rule of option A ⇒ y = 50x + 150

   The rule of option B ⇒

(2) At Week 6 , option A ⇒ $450 , option B ⇒$322.102

(3) See the attached figure and the explanation.

(4) Inputs is the positive integer numbers.

(5) At Week 20 , option A ⇒ $1,150, option B ⇒$1,223.18

Step-by-step explanation:

(1) Determine the rule (or formula) for each sequence. Show your work.

Option A: Receive $200 the first week. Receive an additional $50 for each of the following weeks.

So, this option represents a line with a rate of $50 per week

So, y = mx + c

m = 50

The employees receive $200 the first week ⇒ at x = 1 , y = 200

∴ 200 = 50 + c ⇒ c = 200 - 50 = 150

∴ y = 50x + 150

Option B: Receive $200 the first week. Receive an additional 10% for each of the following weeks.

So, this option represents a geometric series.

The first term is 200 and the common ratio is (1+10% = 1.1)

So,

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(2) Show two calculations using week 6 to convince your friend that both your rules work.

At x = 6

The rule of option A ⇒ y = 50x + 150

So, y = 50 * 6 + 150 = 300 + 150 = $450

The rule of option B ⇒

So,

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(3) Your friend says that because the rules are functions, they can be graphed and must have y-intercepts. Do you agree or disagree with your friend? Explain your thinking.

I agree, See the attached figure.

y-intercept ⇒ The value of y at which x = 0

→The rule of option A ⇒ y = 50x + 150

The rule is graphed with a blue color, and the table with a blue color.

The rule has y-intercept at the point (0,150)

→The rule of option B ⇒

The rule is graphed with a red color, and the table with a red color.

The rule has y-intercept at the point ( 0 , 181.82 )

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(4) Your friend uses your rules to determine the outputs when the inputs are 18.5.  Explain why she cannot use 18.5, and describe types for numbers that CAN be used for inputs?

The variable x represents the weeks and the employer provides the payment options for employees per week.

So, the employer doesn't provide the payments at a half weeks

Therefore, she cannot use 18.5

The types for numbers that CAN be used for inputs is the positive integer numbers x = { 1 , 2 , 3 , 4 , 5 , ........ and so on}

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(5) Use your formulas from #2 to calculate how much each option makes during week 20?

At x = 20

The rule of option A ⇒ y = 50x + 150

So, y = 50 * 20 + 150 = 1,000 + 150 = $1,150

The rule of option B ⇒

So,

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