The question asks which function, $f(x)$ or $g(x)$, has a larger rate of growth.

Let's analyze each function:

Function $g(x) = 2^x - 2$:

This is an exponential function, and we know exponential functions grow rapidly. The base of the exponent is $2$, which means the function grows by a factor of 2 as $x$ increases.

Function $f(x)$:

From the table:

Looking at the values of $f(x)$, it appears that $f(x) = 3^x$. This is also an exponential function, with base $3$, which grows faster than base $2$.

Comparison:

Since $f(x) = 3^x$ has a base of 3 and $g(x) = 2^x - 2$ has a base of 2, $f(x)$ grows faster than $g(x)$. Exponential functions with higher bases grow faster.

Conclusion:

The function $f(x)$ has a larger rate of growth.

Would you like more details on exponential growth, or do you have any other questions?

Here are five related questions to deepen your understanding:

1. How would the growth rate compare if $f(x)$ were $2^x$ instead of $3^x$?
2. Can you explain why exponential functions with higher bases grow faster?
3. How would you find the exact intersection point of $f(x)$ and $g(x)$?
4. What role does the constant term in $g(x) = 2^x - 2$ play in the function's growth?
5. How would the graph of $f(x) = 3^x$ differ from $g(x) = 2^x - 2$?

Tip: The base of an exponential function directly affects how fast it grows—the larger the base, the faster the growth.