Actually they don't. You can not resize a (static) array. What you really want is a dynamic array, an array list or whatever you like to call it. In this case you can double the size of the underlying array when you have to reallocate it and get the amortized runtime down but at the price of using up to twice the memory you need.

Maybe array_append is to blame because its pure existence somewhat implies that you are working with array lists and not with arrays.