Answer:
Option C.
Step-by-step explanation:
The general exponential equation is
[tex]y=ab^x[/tex]
It is given that the graph of exponential function passes through points (4,8) and (6,32). It means the equation of exponential function must be satisfied by these points.
[tex]8=ab^4[/tex] ...(1)
[tex]32=ab^6[/tex] ...(2)
Divide equation (2) by equation (1).
[tex]\dfrac{32}{8}=\dfrac{ab^6}{ab^4}[/tex]
[tex]4=b^2[/tex]
Taking square root on both sides.
[tex]2=b[/tex]
Put b=2 in (1).
[tex]8=a(2)^4[/tex]
[tex]8=16a[/tex]
[tex]\dfrac{8}{16}=a[/tex]
[tex]0.5=a[/tex]
Substitute a=0.5 and b=2 in the given general exponential equation.
[tex]y=0.5(2)^x[/tex]
Therefore, the correct option is C.
