Can someone help me with this one
1 answer:
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Answer:
(, 3)
Step-by-step explanation:
I got 5/2 as my x variable and 3 for my y variable to being the midpoint. In which I added both my x variables provided ( 3 and 2 ) and then I divided them by two to get half of that (since you are looking for in between those two digits technically so you are wanting to find the midpoint or the middle of that line segment). I also did the same with the two y variables as well which were 7 and -1, then I divided both by two to get the variable 3.
1. The first option is represented by a linear function, ∴ y = 50x + 150. The y intercept here is 150, as the first week is 200 dollars, not the 0th week. 200 - 50 = 150.
Given the domain here is 1 - 6 (6 weeks) we can plug in x as 1,2,3 etc and solve for y, completing the table.
Option A :
Week | 1 | 2 | 3 | 4 | 5 | 6 |
Amount Paid | 200 | 250 | 300 | 350 | 400 | 450 |
And for option b we have an exponential function. 1 + 10% = 1 + 0.1 = 1.1. Therefore we have the function ∴ y = 200( 1.1 )^x-1 that models this situation. Remember that we have " x - 1 " as the exponent rather than x, as the first week begins with 200 dollars, not the 0th week.
That gives us the following table,
Option B :
Week | 1 | 2 | 3 | 4 | 5 | 6 |
Amount Paid | 200 | 220 | 242 | 266.2 | 292.82 | 322.102 |
2. (a) We already calculated the " iterative rules " for each sequence in the first part. For your explanation on that behalf, just include the explanation above. Rule of Option A : y = 50x + 150. Rule of Option B : .
(b) Let's take an example week and substitute into our equations to help clarify our friend's doubt. Say week 2...
y = 50(2) + 150 = 100 + 150 = 250 ✓
y = 200( 1.1 )^2-1 = 200( 1.1 )^1 = 200( 1.1 ) = 220 ✓
3. (a) A function is an equation that represents the relation between x and y, which is exactly the purpose of the rules y = 50x + 150, and y = 200( 1.1 )^x-1.
(b) I disagree with my friend. These particular examples do have y - intercepts, but just because a rule is a function, doesn't make it have a y - intercept. There are some exceptions, such as y = 1 / x.
(c) An input such as 18.5 is meaningless, as x represents the weeks. An employer doesn't provide the payments at half weeks.
4. Let's substitute 20 as x,
y = 50 * 20 + 150 = 1,000 + 150 = $1,150
y = 200( 1.1 )^x-1 = 200( 1.1 )^20-1 = 200( 1.1 )^19 = $1,223.1818
The first payment option will provide the greatest total income.