Those fucntions all map quite well to programming or problem space constructs. For example, Polynomial time comes naturaly from nested loops over the input. Exp

Those fucntions all map quite well to programming or problem space constructs. For example, Polynomial time comes naturaly from nested loops over the input. Exponential and factorial complexities come naturally from exhaustive searches over combinatorial explosion, and exponentials also crop up in the context of naive recursion. Logs come from anything that looks like "recursively eliminate a fraction of the possibilities".