# complexity of time constructible function

In field of computational complexity there is a definition of time constructible function.

As example, in any reasonable and general model, functions like $t_1(n) = n^2, t_2(n) = 2^n$, and $t_3(n) = 2^{2^n}$ are computable in $poly(\log t_i (n))$ steps.

I would to know why it's exactly $poly(\log t_i (n))$ steps?

How can I show it?

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