Question

Which is the graph of the sequence defined by the function f(x) = 100(0.5)x - 1?

On a coordinate plane, 4 points are plotted. The points are (0, 100), (1, 50), (2, 25), (3, 12.5).

On a coordinate plane, 4 points are plotted. The points are (1, 100), (2, 50), (3, 25), (4, 12.5).

On a coordinate plane, 3 points are plotted. The points are (0, 100), (2, 90), (4, 80).

On a coordinate plane, 3 points are plotted. The points are (1, 100), (3, 90), (5, 80).

Answer 1

The second graph: the points (1,100), (2,50), (3,25), (4,12.5).

Reason: f(x) = 100(0.5)^{x-1}. For x=1: 100(0.5)^0 = 100; x=2: 100(0.5)^1 = 50; x=3: 25; x=4: 12.5. (If the exponent were x instead of x−1, the first graph would match.)