1:
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.
Make a table to show how much money would be received for both payment options, each week, for 6 weeks.
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.
i need help for number 4
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1:
To create a table showing how much money would be received for both payment options each week for 6 weeks, we can use the given information about Option A and Option B and consider the formula for each option:
Option A:
$200 for the first week
An additional $50 for each following week
Option B:
$200 for the first week
An additional 10% for each following week
Using these formulas, we can create the following table:
Week Option A Option B
------------------------------------
1 $200 $200
2 $250 $220
3 $300 $242
4 $350 $266.20
5 $400 $292.82
6 $450 $322.10
2:
To determine the iterative rules for both sequences, we need to identify the pattern by which each week's payment is increasing.
For Option A, we can see that the payment increases by $50 each week. Therefore, the iterative rule for Option A is:
Payment = $200 + ($50 * (Week - 1))
For Option B, we see that the payment increases by 10% each week. To calculate the iterative rule, we can express the 10% increase as a decimal, 0.1, and multiply it by the previous week's payment. Therefore, the iterative rule for Option B is:
Payment = $200 + (0.1 * (Previous Week's Payment))
To show that both rules work, let's calculate the payments for Week 3 using both rules:
Option A:
Payment = $200 + ($50 * (3 - 1))
= $200 + ($50 * 2)
= $200 + $100
= $300
Option B:
Payment = $200 + (0.1 * (Previous Week's Payment))
= $200 + (0.1 * $242)
= $200 + $24.20
= $224.20
As we can see, the calculated payments match the values in the table from Problem 1. This confirms that the iterative rules are correct.
3:
The rules for Option A and Option B are functions because they assign a unique output (payment amount) to each input (week number). In other words, for every input (week number), there is one and only one output (payment amount) determined by the rule.
Regarding the y-intercepts, we would explain that the rules for Option A and Option B do not have y-intercepts because they both involve a base payment of $200 in the first week. A y-intercept is the point at which a graph intersects the y-axis, and in this case, it represents the payment amount when the week number is zero. However, in these scenarios, the first week is considered the starting point, so the week number cannot be zero.
4:
If an employee plans on quitting after 20 weeks, we need to compare the total income for both payment options after 20 weeks.
For Option A, the total income after 20 weeks can be calculated by using the iterative rule:
Total Income for Option A = ($200 + ($50 * (Week - 1))) * 20
For Option B, the total income after 20 weeks can be calculated by using the iterative rule:
Total Income for Option B = ($200 + (0.1 * (Previous Week's Payment))) * 20
To determine which payment option yields the greatest total income, we can calculate the total income for each option after 20 weeks using the given formulas and compare the results.
By evaluating the two formulas and calculating the values, we can determine which option provides the higher total income after 20 weeks.
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)
Now you can easily make a table. See what you can do with the rest of the questions. If you get stuck, come back and show your attempts.