Mathematics

The key is recognizing that exponential functions have the form $f(x) = a \cdot b^x$ where $a \neq 0$ and $b > 0, b \neq 1$—the variable must be in the exponent, not the base. Once you spot this form, growth vs. decay depends entirely on whether $b > 1$ (growth) or $0 < b < 1$ (decay). Anything else—like $x^2$, $2^x + 3$, or $x^3$—fails the definition and isn't exponential at all.

The key is recognizing that exponential functions have the form $f(x) = a \cdot b^x$ where $a \neq 0$ and $b > 0, b \neq 1$—the variable must be in the exponent, not the base. Once you spot this form, growth vs. decay depends entirely on whether $b > 1$ (growth) or $0 < b < 1$ (decay). Anything else—like $x^2$, $2^x + 3$, or $x^3$—fails the definition and isn't exponential at all.