Let's start by analyzing the data for each problem to determine whether the function is linear, exponential, or neither. Then, I'll find the function that models the data.

We'll begin with problem 25, which shows the following data:

Problem 25:

To check if this is a linear or exponential function, we need to look at how the function behaves:

1. Linear functions have a constant rate of change (the difference between consecutive values of $f(x)$ should be constant).
2. Exponential functions have a constant ratio of consecutive values of $f(x)$ (the ratio between consecutive values should remain constant).

Let's check the differences between consecutive $f(x)$ values to see if the rate of change is constant:

• 6 - 3 = 3
• 12 - 6 = 6
• 18 - 12 = 6
• 30 - 18 = 12

The differences are not constant, so this is not a linear function.

Now, let's check the ratios:

• 6 / 3 = 2
• 12 / 6 = 2
• 18 / 12 = 1.5
• 30 / 18 ≈ 1.67

The ratios are not constant, so this is also not an exponential function. Therefore, the given function is neither linear nor exponential.

Would you like to proceed with the analysis of the other problems (26–32)?