PLEASE HELP ME 100 POINTS WILL GIVE BRAINLIEST PLEASE, its long so be ready for that

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.
(Score for Question 1: _ of 2 points)
1. 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
Option B:
Week 1 2 3 4 5 6
Amount Paid

(Score for Question 2: _ of 6 points)
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.
Answer:

(Score for Question 3: _ of 3 points)
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?
Answer:

(Score for Question 4: _ of 4 points)
4. Use your formulas from #2 to calculate how much each option makes during week 20. (Show your work)
Answer:

To do these word problems, just write equations that reflect the conditions. Once you have the equations, the rest is easy, right? Anyone can solve an equation; the hard part is sorting them out from the words.

So, for #1, we have

A: y = 200 + 50(x-1) = 150+50x

B: y = 200 * 1.10^(x-1)

2: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. Determine the iterative rule for each sequence. Show your work. Your friend trusts your tables in Problem 1, but wonders if you wrote the iterative rules correctly. Show two calculations to convince your friend that both your rules work.

3:Consider the iterative rules you wrote in Problem 2.Explain why the rules are functions. Your friend says that because the rules are functions, they can be graphed and must have y-intercepts. How would you respond to your friend’s comment? Your friend uses your rules to determine the outputs when the inputs are 18.5. Explain why her outputs are meaningless in this situation. What would you tell her about the inputs she can use?

4:The longest amount of time employees can work under Option A or Option B is 20 weeks. After employees work 20 weeks, they can either quit or keep making the same amount they made during Week 20. If an employee plans on quitting after 20 weeks, which payment option gives the greatest total income? Explain.