What will be the time complexity of recurrence relation T(n)=2T(n-1)+c using substitution method?

Question

Where c is constant.

Answer 1

I am getting $\Theta$ (2^n) .

Comments

Unless we approximate we always get $\Theta$. Theta says = while O says <=. So, Theta is more appropriate if it can be used.

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But theta(n) is used when T(n) =Omega(n) as well as O(n) , so seeing the above solution how to conclude that both of them are asymptotically same .

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Here, it is other way. In the proof all statements were "=". So, finally we can say it is $\Theta(2^n)$ and hence $O(2^n)$ and $\Omega(2^n)$.