Let's analyze the table and answer the question step by step.

Table Information:

Step 1: Identify the Type of Growth (Linear vs Exponential)

• Linear growth: The difference between consecutive values is constant.
• Exponential growth: The ratio between consecutive values remains constant.

Let's check if the changes between consecutive years are consistent.

Difference Check (Linear Model):

• $289.74 - 261.29 = 28.45$
• $322.26 - 289.74 = 32.52$
• $356.28 - 322.26 = 34.02$

The differences between consecutive years are not exactly constant, meaning linear growth may not be a perfect fit.

Ratio Check (Exponential Model):

• $\frac{289.74}{261.29} \approx 1.109$
• $\frac{322.26}{289.74} \approx 1.112$
• $\frac{356.28}{322.26} \approx 1.105$

The ratios are quite close to each other (around 1.11), suggesting that the data follows exponential growth.

Step 2: Complete the Answer

• Exponential function would better model the data because as $x$ increases, the y values change by a constant ratio.
• The growth factor of this function is approximately 1.11.

Do you want further details on how we arrived at these conclusions or need help with submitting the answer?

Here are 5 follow-up questions:

1. What is the general formula for an exponential function?
2. How can we fit an exact exponential equation to this data?
3. How do you distinguish between linear and quadratic models?
4. What would the predicted value be for year 5 using the exponential model?
5. How can you calculate the percent increase for each year?

Tip: When checking for exponential growth, calculating both differences and ratios helps confirm the correct model.