Question

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

Explanation:

Evaluate the function at \(x = 1\)

$$ f(1) = 100(0.5)^{1-1} = 100(0.5)^0 = 100(1) = 100 $$

Evaluate the function at \(x = 2\)

$$ f(2) = 100(0.5)^{2-1} = 100(0.5)^1 = 50 $$

Identify the matching graph

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

Answer:

• (A) Graph with points (0, 100), (1, 50), (2, 25), (3, 12.5)
• (B) Graph with points (1, 100), (2, 50), (3, 25), (4, 12.5) (Correct answer)
• (C) Graph with points (0, 100), (2, 90), (4, 80)
• (D) Graph with points (1, 100), (3, 90), (5, 80)