Question

the graph shows the total monthly sales as a function of the number of cake tiers. which statement is true? as the number of cake tiers decreases, the total monthly sales increase without bound. as the number of cake tiers increases without bound, the total monthly sales decrease without bound. as the number of cake tiers increases without bound, the total monthly sales increase without bound. there is no limit to the number of cake tiers, but there is a limit to the total monthly sales.

Explanation:

Step1: Analyze the graph trend

The graph shows a curve where as \(x\) (number of cake tiers) increases, \(y\) (total monthly sales) also increases.

Step2: Evaluate each statement

• For the first statement: As \(x\) (number of cake tiers) decreases, \(y\) (total monthly sales) should decrease (opposite of the graph trend), so it is false.
• For the second statement: As \(x\) (number of cake tiers) increases without bound, \(y\) (total monthly sales) should increase (from the graph trend, not decrease), so it is false.
• For the third statement: As \(x\) (number of cake tiers) increases without bound, \(y\) (total monthly sales) increases without bound (matches the graph's upward - trending nature), so it is true.
• For the fourth statement: The graph shows \(y\) (total monthly sales) increasing as \(x\) (number of cake tiers) increases, so there is no upper limit on \(y\) shown, making this statement false.

Answer:

As the number of cake tiers increases without bound, the total monthly sales increase without bound.