The problem involves comparing a linear function $f(x) = 75x + 300$ and an exponential function $g(x) = 300(1.1)^x$, based on the given table values. The goal is to determine the $x$-value at which the exponential function begins to show more growth than the linear function.

Observations from the Table:

At $x = 18$, the exponential function $g(x) = 300(1.1)^x$ surpasses the linear function $f(x) = 75x + 300$ because $1667.98 > 1650$.

Thus, the exponential function shows more growth than the linear function at $x = 18$.

Would you like a detailed explanation of how this conclusion is derived?

Here are five related questions to deepen understanding:

1. How can you identify the growth rate difference between linear and exponential functions?
2. Why does an exponential function eventually surpass a linear function in terms of growth?
3. Can you calculate when an exponential function overtakes a linear one for different growth rates?
4. How does changing the base of an exponential function affect when it surpasses a linear function?
5. What other types of functions grow faster than linear but slower than exponential?

Tip: Exponential functions grow at a constant percentage rate, while linear functions grow at a constant amount per unit increase in $x$.