the table represents an exponential function. what is the multiplicative rate of change of the function? 0.2…

Explanation:

Step1: Calculate the ratio of consecutive (y)-values

For an exponential function (y = a\cdot b^{x}), the multiplicative rate of change (b) can be found by (\frac{y_{n + 1}}{y_{n}}). Take (y_1=0.25) (when (x = 1)) and (y_2 = 0.125) (when (x=2)). [b=\frac{y_2}{y_1}=\frac{0.125}{0.25}] [b = 0.5]

Step2: Verify with another pair of (y)-values

Take (y_2 = 0.125) (when (x = 2)) and (y_3=0.0625) (when (x = 3)). [b=\frac{y_3}{y_2}=\frac{0.0625}{0.125}] [b = 0.5] Take (y_3 = 0.0625) (when (x = 3)) and (y_4=0.03125) (when (x = 4)). [b=\frac{y_4}{y_3}=\frac{0.03125}{0.0625}] [b = 0.5]

Answer:

(0.5)