Question

because a picture frame includes a border, the picture must be smaller in area than the entire frame. the table below shows the relationship between picture area and frame length for a particular line of frames. is this an exponential relationship?
frame length (inches) | picture area (in²)
5 | 6
6 | 12
7 | 20
8 | 30
9 | 42
choose the correct words or phrases to complete the statements.

• the picture area select choice increase by a common ratio.
• so, the relationship select choice exponential.

Explanation:

Step1: Check ratio of consecutive areas

$\frac{12}{6}=2$, $\frac{20}{12}\approx1.67$, $\frac{30}{20}=1.5$, $\frac{42}{30}=1.4$

Step2: Analyze the ratios

The ratios are not constant.

Step3: Define exponential relationship

Exponential relationships require a constant common ratio between consecutive terms.

Answer:

• The picture area does not increase by a common ratio.
• So, the relationship is not exponential.