To determine if the cost of oranges can be modeled by a linear function, we need to check if the rate of change in cost per unit of oranges is constant.
Let's calculate the cost per orange for each of the given quantities:
1 orange: $0.89
3 oranges: $2.67 → Cost per orange = $2.67 / 3 = $0.89
5 oranges: $4.45 → Cost per orange = $4.45 / 5 = $0.89
9 oranges: $8.01 → Cost per orange = $8.01 / 9 ≈ $0.89
12 oranges: $10.68 → Cost per orange = $10.68 / 12 = $0.89
It appears that the cost per orange remains consistent at approximately $0.89 as the quantity increases. However, let’s look at the differences in costs for increments in the number of oranges to confirm the linearity:
- From 1 to 3 oranges: $2.67 - $0.89 = $1.78 (cost for 2 extra oranges)
- From 3 to 5 oranges: $4.45 - $2.67 = $1.78 (cost for 2 extra oranges)
- From 5 to 9 oranges: $8.01 - $4.45 = $3.56 (cost for 4 extra oranges)
- From 9 to 12 oranges: $10.68 - $8.01 = $2.67 (cost for 3 extra oranges)
The increments are not consistent, indicating a variable rate of change in cost with respect to the number of oranges.
Therefore, the correct response is:
No, because the rate of growth is a variable rate of change.
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