Exponential functions and linear functions are really cool because they grow in very different ways. Let’s look at how they compare:

1. Linear Growth: Linear functions, like $f(x) = mx + b$, go up by a constant amount. For example, if $m = 2$, this means that no matter what value $x$ has, the function adds 2 for every increase of 1 in $x$. So, if you were to draw a graph of this function, it would be a straight line.

2. Exponential Growth: On the other hand, exponential functions, like $g(x) = a \cdot b^x$, grow much faster. When $b$ is greater than 1, as $x$ gets bigger, the function can double or even triple really quickly. For example, with $a = 1$ and $b = 2$, the numbers jump from $1$ to $2$ to $4$ to $8$, and keep going up!

3. Visual Difference: If you draw both types of functions, you’ll see the linear function looks flat and straight, while the exponential function curves sharply upward.

In short, linear functions are steady and predictable, but exponential functions can surprise us with their rapid growth!