the table represents an exponential function. what is the multiplicative rate of change of the function? 1 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=2) (when (x = 1)) and (y_2=\frac{2}{5}) (when (x = 2)). [b=\frac{y_2}{y_1}=\frac{\frac{2}{5}}{2}] [=\frac{2}{5}\times\frac{1}{2}] [=\frac{1}{5}] Check with another pair: (y_2=\frac{2}{5}) and (y_3=\frac{2}{25}) [b=\frac{y_3}{y_2}=\frac{\frac{2}{25}}{\frac{2}{5}}] [=\frac{2}{25}\times\frac{5}{2}] [=\frac{1}{5}]

Answer:

(\frac{1}{5})