Let's analyze and complete the table for the two functions given:

• $f(x) = 4^x$
• $g(x) = x + 8$

The table values need to be calculated for $x = 1, 2, 3, 4$.

For $f(x) = 4^x$:

1. $f(1) = 4^1 = 4$
2. $f(2) = 4^2 = 16$
3. $f(3) = 4^3 = 64$
4. $f(4) = 4^4 = 256$

For $g(x) = x + 8$:

1. $g(1) = 1 + 8 = 9$
2. $g(2) = 2 + 8 = 10$
3. $g(3) = 3 + 8 = 11$
4. $g(4) = 4 + 8 = 12$

Completed Table:

Which function eventually exceeds the other?

While $g(x)$ initially grows faster than $f(x)$, after $x = 2$, $f(x)$ starts to exceed $g(x)$. For large values of $x$, $f(x) = 4^x$ will grow exponentially faster than the linear function $g(x) = x + 8$.

Let me know if you'd like further clarification or details!

Five follow-up questions:

1. What is the general difference between exponential and linear functions?
2. How would the table change if we evaluated $x = 0$ for both functions?
3. What happens to $f(x)$ and $g(x)$ as $x$ becomes very large?
4. Can you compare the rate of growth of $4^x$ to that of other exponential functions, like $2^x$?
5. What is the significance of the intersection point between the two functions?

Tip: Exponential functions like $4^x$ grow much faster than linear functions like $x + 8$ after a certain point.