Hey guys! Please help me with these last few questions! I have finished the rest, but I need help writing out these below. Thank you so much!
Is the relationship a function?
x: 0, 1, 2, 3
y: 5, 2, -1, -4
Four sisters, Jenny, Julie, Jolie and Jada, are saving money for summer vacation. Their mom gets them started by giving the older sisters, Jenny and Jada, $25 each and the younger sisters $15 each. Each sister will put part of the pay from their after school job in the account each week.
Jenny and Jolie will each deposit $8 per week. Julie and Jada will each deposit $5 per week.
Make a table for the total savings for each sister.
Week: 0, 1, 2, 3, 4, 5, 6
Jenny:
Julie:
Jolie:
Jada:
Model each sister's savings plan using an equation in the form y = mx + b.
Jenny:
Julie:
Jolie:
Jada:
Will Jolie ever have more than Jenny?
Will Jolie ever have more than Jada?
I'm really bad at functions right now, so if someone could help me asap that would be great. Thank you so much again!
- lue
since each x is used only once, it is a function
if this was hard, you really need to review the properties of a function.
Just fill in the table with the given starting values, and then just add multiples of 8 and 5, since that is how much each one earns per week. It should be clear whether the amounts match at some point.
Is the relationship a function?
To determine if the relationship is a function, we need to check if each input value (x) is associated with exactly one output value (y).
Looking at the given x and y values:
x: 0, 1, 2, 3
y: 5, 2, -1, -4
We can see that each value of x is associated with exactly one value of y. Hence, the relationship is a function.
Make a table for the total savings for each sister.
Week: 0, 1, 2, 3, 4, 5, 6
Jenny: $25, $33, $41, $49, $57, $65, $73
Julie: $15, $20, $25, $30, $35, $40, $45
Jolie: $15, $23, $31, $39, $47, $55, $63
Jada: $25, $33, $41, $49, $57, $65, $73
Model each sister's savings plan using an equation in the form y = mx + b.
Jenny: y = 8x + 25
Julie: y = 5x + 15
Jolie: y = 8x + 15
Jada: y = 5x + 25
Will Jolie ever have more than Jenny?
To determine if Jolie will ever have more savings than Jenny, we can compare their equations:
Jenny: y = 8x + 25
Jolie: y = 8x + 15
By looking at the equations, we can see that Jolie starts with a lower constant value (b) than Jenny. However, since both have the same rate of increase (m = 8), eventually Jolie's savings will surpass Jenny's.
Will Jolie ever have more than Jada?
To determine if Jolie will ever have more savings than Jada, we can compare their equations:
Jolie: y = 8x + 15
Jada: y = 5x + 25
Looking at the equations, we can see that Jada starts with a higher constant value (b) than Jolie. Additionally, Jolie has a higher rate of increase (m = 8) compared to Jada (m = 5). Therefore, Jolie will surpass Jada's savings at some point.
I hope this helps! Let me know if you have any further questions.
To determine if the relationship between x and y is a function, you need to check if each value of x is associated with only one unique value of y. In other words, if there are no repeated x-values with different y-values.
Looking at the given x and y values:
x: 0, 1, 2, 3
y: 5, 2, -1, -4
Based on the given values, we can see that each x-value is associated with one unique y-value. Therefore, the relationship is a function.
Now let's move on to the next question about the total savings for each sister.
Week: 0, 1, 2, 3, 4, 5, 6
Jenny:
Julie:
Jolie:
Jada:
To find the total savings for each sister, we need to calculate the sum of the initial amount given by their mom and the weekly deposits made by the sisters. Let's fill in the table:
Week: 0, 1, 2, 3, 4, 5, 6
Jenny: 25, 33, 41, 49, 57, 65, 73
Julie: 15, 20, 25, 30, 35, 40, 45
Jolie: 15, 23, 31, 39, 47, 55, 63
Jada: 25, 30, 35, 40, 45, 50, 55
Next, we are asked to model each sister's savings plan using an equation in the form y = mx + b, where y represents the total savings and x represents the number of weeks.
Jenny's savings plan: y = 8x + 25
Julie's savings plan: y = 5x + 15
Jolie's savings plan: y = 8x + 15
Jada's savings plan: y = 5x + 25
To determine if Jolie will ever have more than Jenny or more than Jada, we need to compare their savings over time. Looking at their respective equations, we can see that the coefficient of x for Jolie (8) is greater than that of Jenny (8) and Jada (5). Therefore, Jolie will have more savings than both Jenny and Jada at some point in time.
I hope this helps! Let me know if you have any further questions.