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? 5 2 2.5 0.5

Explanation:

Step1: Recall exponential function form

The general form of an exponential function is \( f(x) = a(b)^x \), where \( a \) is the initial value and \( b \) is the multiplicative rate of change.

Step2: Identify \( b \) in given function

The given function is \( f(x) = 10(0.5)^x \). Comparing with \( f(x) = a(b)^x \), we see that \( b = 0.5 \). So the multiplicative rate of change is \( 0.5 \).

Answer:

0.5 (the option with 0.5)