The problem asks to determine a linear function $C(x)$ representing the cost of tuition per credit hour at a university, where $x$ is the number of years since 1990.

From the image, the cost of tuition in 1990 was $97 per credit hour, and by 1997 it had risen to $188 per credit hour.

First, we calculate the rate of change per year:

• 1990 corresponds to $x = 0$
• 1997 corresponds to $x = 7$
• Change in tuition cost from 1990 to 1997 is $$$188 - $97 = $91$$
• Rate of change per year $= \frac{91}{7} \approx 13$ dollars per year

Thus, the slope $m$ of the linear function $C(x)$ is approximately 13.

Using the point-slope form of the linear equation: $C(x) = m(x - x_1) + y_1$ where $(x_1, y_1)$ is the point (0, 97), substituting the known values: $C(x) = 13(x - 0) + 97$ $C(x) = 13x + 97$

To find the cost of tuition in 2003:

• 2003 corresponds to $x = 2003 - 1990 = 13$ $C(13) = 13(13) + 97 = 169 + 97 = 266$

Therefore, the linear function is $C(x) = 13x + 97$, and the tuition cost in 2003 would be $266 per credit hour.

Do you need any further explanations or details on how these calculations were done?

Here are some additional questions you might consider:

1. How would you modify the equation if the rate of tuition increase changed?
2. What would be the tuition in 2020 based on this model?
3. How would the equation change if we included more data points from other years?
4. Can you apply this model to predict future tuition costs? What factors might affect its accuracy?
5. How could you use this model in budget planning for future college expenses?

Tip: Always verify the units of your slope when working with real-world linear models to ensure they match the context of the problem.