The difference between [tex]\frac{1}{2}e^{x-4}[/tex] and [tex]e^{x-4}[/tex] is that the first equation is only half of the second equation. When we multiplied [tex]e^{x-4}[/tex] by [tex]\frac{1}{2}[/tex], the remaining result became half of [tex]e^{x-4}[/tex]. Hope this helps!