Question

The cost to mail a package that weighs x pounds at AAA
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Shipping is represented by the table.

Weight (in lbs.) 4 5 6 7 8
Cost (in dollars) 5.56 6.95 8.34 9.73 11.12
What type of function could be used to model the cost to mail a package as a function of weight?

(1 point)
Responses

exponential decay function
exponential decay function

exponential growth function
exponential growth function

linear function
linear function

quadratic function

Answer 1

To determine the type of function that models the cost to mail a package as a function of weight, we can look at the data points provided:

- For 4 lbs, the cost is $5.56
- For 5 lbs, the cost is $6.95
- For 6 lbs, the cost is $8.34
- For 7 lbs, the cost is $9.73
- For 8 lbs, the cost is $11.12

Looking at the costs, we can see that as the weight increases, the cost also increases. The increments in cost, however, are not consistent (they increase by different amounts), which suggests that the relationship is not linear (which would have equal increments).

To further analyze the pattern:

- From 4 to 5 lbs: increase of $1.39
- From 5 to 6 lbs: increase of $1.39
- From 6 to 7 lbs: increase of $1.39
- From 7 to 8 lbs: increase of $1.39

All increments are consistent (+$1.39), indicating a linear relationship.

Therefore, the appropriate function to model the cost to mail a package as a function of weight is a **linear function**.

**Response: linear function**.