Time Complexity of an recursive Algorithm

Goodmorning, I have to analyze the time complexity of this algorithm:

Pseudocode:

minMax(vet, b, e) //b->index of the first element; e->index of the last element {         if(e-b <= 1)         {                 return <min(vet[b], vet[e]), max(vet[b], vet[e])>;         }         else         {                 p = [(b+e)/2];                 <min,max> = minMax(vet, b, p);                 <min2,max2> = minMax(vet, p+1, e);                 return <min(min, min2), max(max1, max2)>;         } } 

Time complexity:

$ T(n) = 2^{i-1}T(n/2^{i-1})+2^{i-1}c$

$ n = 2^i$

$ i = log_2(n)$

$ T(n) = \frac{n}{2}T(2)+\frac{n}{2}c = $

$ = n+\frac{n}{2}c = \frac{3n}{2}c \in Θ(n)$

are the steps correct?