Answer:
The correct option is B.
Step-by-step explanation:
The general form of an exponential function is
[tex]g(x)=ab^x[/tex] .... (1)
Where, a is initial value and b is growth or decay factor.
If b>1, then it is an increasing function and if 0<b<1, then it is a decreasing function.
The given function is
[tex]f(x)=6\cdot (0.4)^x[/tex] .... (2)
From (1) and (2) it is clear that
[tex]a=6,b=0.4[/tex]
The value of a is 6. It means the initial value or y-intercept of the function is 6.
The value of b is 0.4, which is less than 1. It means the function is a decreasing function.
Graph B represent a decreasing function with initial value 6. Therefore the correct option is B.
