which is the graph of the sequence defined by the function $f(x) = 100(0.5)^{x - 1}$?

Explanation:

Step1: Calculate f(1)

Substitute $x=1$ into $f(x)$: $$f(1)=100(0.5)^{1-1}=100(0.5)^0=100\times1=100$$

Step2: Calculate f(2)

Substitute $x=2$ into $f(x)$: $$f(2)=100(0.5)^{2-1}=100(0.5)^1=100\times0.5=50$$

Step3: Calculate f(3)

Substitute $x=3$ into $f(x)$: $$f(3)=100(0.5)^{3-1}=100(0.5)^2=100\times0.25=25$$

Step4: Match points to graphs

The sequence has points $(1,100)$, $(2,50)$, $(3,25)$, which matches the middle graph.

Answer:

The middle graph (with points $(0,100)$, $(1,50)$, $(2,25)$, $(3,12.5)$)