Question

what is the decay factor of the exponential function represented by the table?

\

$$\begin{array}{|c|c|} \\hline x & f(x) \\\\ \\hline -1 & 18 \\\\ \\hline 0 & 6 \\\\ \\hline 1 & 2 \\\\ \\hline 2 & \\frac{2}{3} \\\\ \\hline \\end{array}$$

• \\(\frac{1}{3}\\)
• \\(\frac{2}{3}\\)
• \\(2\\)
• \\(6\\)

Explanation:

Identify the exponential function form

$$ f(x) = a \cdot b^x $$

Calculate the ratio of consecutive terms

$$ b = \frac{f(x+1)}{f(x)} = \frac{f(0)}{f(-1)} = \frac{6}{18} = \frac{1}{3} $$

Verify with other consecutive terms

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Answer:

• (A) \(\frac{1}{3}\) (Correct answer)
• (B) \(\frac{2}{3}\)
• (C) 2
• (D) 6