The graphs provided compare the functions $y = 4x$ (linear) and $y = 4^x$ (exponential).

Analysis of Growth:

• Linear Function: $y = 4x$ grows at a constant rate. This is shown by the straight line in blue, indicating a steady, predictable increase as $x$ increases.
• Exponential Function: $y = 4^x$ grows at an increasing rate, starting slower but eventually surpassing the linear function as $x$ gets larger. The green curve in the graph shows this rapid growth.

General Growth Comparison:

• At first, $y = 4x$ grows faster (as seen for lower values of $x$). But as $x$ increases, the exponential function $y = 4^x$ eventually grows faster than $y = 4x$.

Conclusion:

The correct statement is: The function $y = 4^x$ is growing faster than $y = 4x$.

Would you like further details on why exponential functions grow faster over time compared to linear functions?

Here are five related questions to consider:

1. How do we mathematically compare growth rates of linear vs exponential functions?
2. At what exact point does the function $y = 4^x$ surpass $y = 4x$?
3. What are the key differences between linear and exponential growth?
4. How does the base of the exponential function (4 in $4^x$) affect the speed of growth?
5. How would the graphs change if we used different constants in the linear or exponential equations?

Tip: Exponential growth eventually overtakes linear growth, no matter how large the slope of the linear function is. This is a key feature of exponential functions.