Mathematics

The key to understanding exponential functions is recognizing that the base (3 here) tells you the growth factor — how much the output multiplies each time $x$ increases by 1. The coefficient (2) is just a vertical stretch that scales all outputs. To work with this function, you'll use properties like $3^{a+b} = 3^a \cdot 3^b$ and remember that exponential growth is fundamentally different from linear change — it accelerates.

The key to understanding exponential functions is recognizing that the base (3 here) tells you the growth factor — how much the output multiplies each time $x$ increases by 1. The coefficient (2) is just a vertical stretch that scales all outputs. To work with this function, you'll use properties like $3^{a+b} = 3^a \cdot 3^b$ and remember that exponential growth is fundamentally different from linear change — it accelerates.