which is the graph of the sequence defined by the function f(x) = 100(0.5)^(x - 1)?
which is the graph of the sequence defined by the function f(x) = 100(0.5)^(x - 1)?
Answer
Explanation:
Step1: Find the first - term
When (x = 1), substitute (x=1) into (f(x)=100(0.5)^{x - 1}). Then (f(1)=100(0.5)^{1 - 1}=100(0.5)^{0}=100\times1 = 100).
Step2: Find the second - term
When (x = 2), substitute (x = 2) into (f(x)=100(0.5)^{x - 1}). Then (f(2)=100(0.5)^{2 - 1}=100\times0.5=50).
Step3: Find the third - term
When (x = 3), substitute (x = 3) into (f(x)=100(0.5)^{x - 1}). Then (f(3)=100(0.5)^{3 - 1}=100\times(0.5)^{2}=100\times0.25 = 25).
Step4: Find the fourth - term
When (x = 4), substitute (x = 4) into (f(x)=100(0.5)^{x - 1}). Then (f(4)=100(0.5)^{4 - 1}=100\times(0.5)^{3}=100\times0.125 = 12.5).
The points ((1,100)), ((2,50)), ((3,25)), ((4,12.5)) should be on the graph of the sequence. So the graph with the points ((1,100)), ((2,50)), ((3,25)), ((4,12.5)) is the correct one.
Answer:
The graph with points ((1,100)), ((2,50)), ((3,25)), ((4,12.5)) (the first graph among the options shown in the picture).