Answer
Algorithms of $\Theta\left(n^{2}\right)$ are polynomial algorithms because $n$ is raised to a constant power. An algorithm of $\Theta\left(2^{n}\right)$ is an exponential algorithm. It is the nonconstant exponent that makes this value grow so quickly, as opposed to polynomial algorithms. An algorithm of $\Theta\left(n^{n}\right)$ would still be considered an exponential algorithm because its exponent is $n .$ In fact, such an algorithm grows even faster than one of order $2^{n}$ because of the nonconstant base.
Work Step by Step
Algorithms of $\Theta\left(n^{2}\right)$ are polynomial algorithms because $n$ is raised to a constant power. An algorithm of $\Theta\left(2^{n}\right)$ is an exponential algorithm. It is the nonconstant exponent that makes this value grow so quickly, as opposed to polynomial algorithms. An algorithm of $\Theta\left(n^{n}\right)$ would still be considered an exponential algorithm because its exponent is $n .$ In fact, such an algorithm grows even faster than one of order $2^{n}$ because of the nonconstant base.
