The table in the image provides data for an investment's value over time. Here's the data:

The goal is to determine whether the best-fitting function for this data is linear or exponential.

To begin, we can examine the pattern in the changes between consecutive years.

• From year 1 to year 2: 22,910.30 - 19,962.01 = 2,948.29
• From year 2 to year 3: 26,426.21 - 22,910.30 = 3,515.91
• From year 3 to year 4: 30,481.40 - 26,426.21 = 4,055.19

Notice that the difference between values is increasing, which suggests exponential growth rather than linear growth. In a linear function, the changes between consecutive values should be constant.

Conclusion:

The function that best fits this data is exponential because, as $x$ (the number of years) increases, the $y$ (value of the investment) increases at an accelerating rate.

Tip:

For exponential functions, the ratio between successive values typically increases, while in linear functions, the difference between values remains constant.

Would you like more details or have any questions? Here are some related questions to explore further:

1. How do you determine the exact exponential function for this data?
2. How does the concept of exponential growth differ from linear growth in real-world applications?
3. What are the properties of an exponential function that make it a good fit for investment growth?
4. Can you explain the concept of compound interest, which is related to exponential growth?
5. How do you calculate the rate of growth in exponential functions?

Let me know if you'd like to dive into any of these!