Exponents are a helpful way to compare how quickly different functions grow. Here are some important points to understand:

1. Understanding Growth Rates:

   • Linear functions, like $f(x) = 2x$, grow at a steady pace.
   • Quadratic functions, such as $g(x) = x^2$, grow faster because they include a squared term.
   • Exponential functions, for example, $h(x) = 3^x$, grow very quickly, especially as $x$ gets larger.

2. Statistical Comparison:

   • When $x = 1$:
     • $f(1) = 2$
     • $g(1) = 1$
     • $h(1) = 3$
   • When $x = 5$:
     • $f(5) = 10$
     • $g(5) = 25$
     • $h(5) = 243$
   • You can see that $h(5)$ is much bigger than the other two.

3. Conclusion:

   • As $x$ gets larger, exponential functions grow much faster than both linear and quadratic functions. This shows just how powerful exponents are when we look at growth!