Question

Mallory puts $1.00 in a jar. The following week, she puts 2 times that original amount in the jar. For each of the next six weeks, Mallory continues to double the amout of money she places in her savings jar each week.
Determine if the relationship is linear or nonlinear. Explain your choice using examples with ordered pairs. (week, amount)

Answer 1

The relationship of the ordered pair that represents Mallory savings is a nonlinear relationship.

Let x represents the number of weeks, and y represents the amount put in the jar, each week.

So, we have the following highlights for 6 weeks.

• Week 1: (1, 1)
• Week 2: (2,2)
• Week 3: (3,4)
• Week 4: (4,8)
• Week 5: (5,16)
• Week 6: (6,32)

The ordered pairs can then be represented as:

$(x,y) = (1,1)(2,2)(3,4)(4,8)(5,16)(6,32)$

As the x values increase, the y values increase too, but the y values do not increase at a constant rate.

This means that the relationship is not linear; it is an exponential relationship.

Hence, the relationship is a nonlinear relationship.

Read more about linear relationships at:

brainly.com/question/7040405

Answer 2

We want to see if the relationship between the number of weeks and the money put in the jar is linear or not, we will see that this is not a linear equation (it is exponential).

So a linear relation is something like:

y = a*x + b

Note that for any value of x, an increase of 1 unit gives:

y = a*(x+ 1) + b = (a*x + b) + a

So for increases of 1 unit in the x-value, we have increases of "a" units on the y-value.

In the given situation we have:

• In week 1 she puts $1.00 in the jar.
• In week 2 she puts $2.00 in the jar (now the jar has $3.00 in it)
• In week 3 she puts $4.00 in the jar (now the jar has $7.00 on it)
• In week 4 she puts $8.00 in the jar (now the jar has $15.00 on it)

and so on.

Writing that as points we have:

(1, $1)

(2, $3)

(3, $7)

(4, $15)

Notice that for equal increases in the x-value, (increases of 1 unit) we don't equal increases in the y-value (first increases by $2, then by $4, etc...) So this is not a linear equation, this is actually exponential.

If you want to learn more, you can read:

brainly.com/question/19770987