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The table shows the linear relationship between the balance saved each week. What is the rate of change in terms of balance (in dollars) with respect to the number of weeks?

User Icon for Bot GPT 3.5 Bot GPT 3.5 answered
9 months ago

To determine the rate of change in terms of balance (in dollars) with respect to the number of weeks, we need to find the slope of the linear relationship between the two variables.

The slope can be calculated using the formula:
slope = (change in y)/(change in x)

In this case, the change in y represents the change in balance (in dollars) and the change in x represents the change in the number of weeks.

Since all we have is a statement that "the table shows the linear relationship between the balance saved each week," without the specific values of the table, it is not possible to determine the rate of change in terms of balance with respect to the number of weeks.

User Icon for YUUU YUUU answered
9 months ago

week 0 1 3 6 8 13

balance 32 39 53 74 88 123

User Icon for Bot GPT 3.5 Bot GPT 3.5 answered
9 months ago

We can use the values from the table to determine the rate of change in terms of balance (in dollars) with respect to the number of weeks.

First, we can calculate the change in balance (Δy) and the change in the number of weeks (Δx) between consecutive points in the table:

Δy = balance2 - balance1
Δx = week2 - week1

Using the table values, we can calculate the differences:
Δy1 = 39 - 32 = 7
Δx1 = 1 - 0 = 1

Δy2 = 53 - 39 = 14
Δx2 = 3 - 1 = 2

Δy3 = 74 - 53 = 21
Δx3 = 6 - 3 = 3

Δy4 = 88 - 74 = 14
Δx4 = 8 - 6 = 2

Δy5 = 123 - 88 = 35
Δx5 = 13 - 8 = 5

Next, we can calculate the rate of change (slope) using the formula:
slope = (Δy) / (Δx)

For each pair of differences, we can calculate the slope:
Slope1 = Δy1 / Δx1 = 7 / 1 = 7
Slope2 = Δy2 / Δx2 = 14 / 2 = 7
Slope3 = Δy3 / Δx3 = 21 / 3 = 7
Slope4 = Δy4 / Δx4 = 14 / 2 = 7
Slope5 = Δy5 / Δx5 = 35 / 5 = 7

Therefore, the rate of change in terms of balance (in dollars) with respect to the number of weeks is a constant value of 7 dollars per week.