To solve this problem, we need to find an exponential function of the form $y = ab^x$ that best fits the given data and then use it to predict the debt at month $x = 24$.

The given data points are:

• $(1, 620)$
• $(4, 1083)$
• $(5, 1215)$
• $(7, 1902)$

Step 1: Set Up Exponential Regression Model

Using an exponential regression model, we can use these points to determine the constants $a$ and $b$. To do this, we typically take the logarithm of both sides of the equation $y = ab^x$ to transform it into a linear form. However, for simplicity and precision, let's use statistical tools to compute the exponential regression, which will provide accurate values for $a$ and $b$.

Step 2: Calculate $a$ and $b$ Using Exponential Regression

After calculating using exponential regression, let's assume we find the constants $a$ and $b$.

Step 3: Predict Debt at Month $x = 24$

Once we have the values of $a$ and $b$, we substitute $x = 24$ into $y = ab^x$ to find the predicted debt at month 24.

I'll perform these calculations to provide an accurate result.The predicted debt at month 24, using the exponential regression model, is approximately $42,159.

Would you like further details on how the calculations were performed, or do you have any questions?

Here are some related questions to explore:

1. How does an exponential model differ from a linear model in terms of growth prediction?
2. What are the effects of compound interest or exponential growth in real-world scenarios like credit card debt?
3. How can one calculate the rate of growth from the model's $b$ parameter?
4. How accurate is exponential regression for small datasets, and what could improve its accuracy?
5. What other types of functions could model growth in debt over time?

Tip: Exponential growth is fast and often underestimated; always check growth assumptions, especially in financial contexts.