Answer:
[tex]y=3(2)^{x-5}+6[/tex]
Step-by-step explanation:
Let the equation of the exponential function with base 2 is,
[tex]y=a(2)^{x+c}+d[/tex]
Here, a = vertical stretch
c = Horizontal shift
d = Vertical shift
If this function has a vertical stretch by a factor of 3,
Equation will be,
[tex]y=3(2)^{x+c}+d[/tex]
If this function has a shift of 5 to the right,
Equation of the function will be,
[tex]y=3(2)^{x-5}+d[/tex]
If this function has a shift of 6 units upwards,
[tex]y=3(2)^{x-5}+6[/tex]
