It is required to choose the graph that correctly represents the function:
[tex]f(x)=3\left(\frac{1}{2}\right)^x[/tex]
Recall that an exponential function is of the form:
[tex]f(x)=a(b)^x[/tex]
With b greater than 0, but not equal to 1.
Recall also that if b<1, then the exponential function is a decreasing function.
Hence, the possible graphs are C or D.
Calculate the y-intercept by substituting x=0 into the equation, and then compare with the graphs C or D:
[tex]f(0)=3\left(\frac{1}{2}\right)^0=3\cdot1=3[/tex]
It follows that the y-intercept is 3.
Notice that only graph C has a y-intercept of 3 between C and D.
Hence, the correct graph is graph C.
The correct graph is graph C.
