Question

the curve through the ordered pairs (0, 10), (1, 5), and (2, 2.5) can be represented by the function \\(f(x) = 10(0.5)^x\\).
what is the multiplicative rate of change of the function?

\\(\bigcirc\\) 0.5
\\(\bigcirc\\) 2
\\(\bigcirc\\) 2.5
\\(\bigcirc\\) 5

Explanation:

Identify the standard exponential function form

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

Determine the base of the given function

$$
LATEXBLOCK0
$$

Relate the base to the multiplicative rate of change

$$ \text{Multiplicative Rate of Change} = b = 0.5 $$

Answer:

• (A) 0.5 (Correct answer)
• (B) 2
• (C) 2.5
• (D) 5