Question

A coffee shop has the latte menu shown below.

Size (Oz) Cost($)
Short(10) $4.29
Tall(16) $4.59
Grande(20) $ $4.89
Super(24) $5.39
Consider the cost of a latte, in dollars, as a function of the size of the latte, measured in fluid ounces. Is this a linear function? Explain

Answer 1

The cost per ounce of a latte decreases as the size of the latte increases, indicating that the cost as a function of size is not a linear function due to the lack of a constant rate of change.

Step-by-step explanation:

When determining whether the cost of a latte as a function of its size is a linear function, one should check for a constant rate of change in price per unit of increase in size. Calculating the cost per ounce for each size and examining its consistency provides insight into whether the function is linear.

• For the Short (10 oz) latte, the cost per ounce is $4.29 / 10 oz = $0.429.
• For the Tall (16 oz) latte, the cost per ounce is $4.59 / 16 oz = $0.286.
• For the Grande (20 oz) latte, the cost per ounce is $4.89 / 20 oz = $0.2445.
• For the Super (24 oz) latte, the cost per ounce is $5.39 / 24 oz = $0.2246.

The cost per ounce decreases as the size increases, which means the relationship between size and cost is not characterized by a constant rate of change. Consequently, the cost of a latte in relation to its size is not a linear function. Rather, it exhibits a decreasing rate as size increases.