Question

the table represents an exponential function.

x	y
2	\\(\frac{2}{5}\\)
3	\\(\frac{2}{25}\\)
4	\\(\frac{2}{125}\\)

what is the multiplicative rate of change of the function?
\\(\circ\\) \\(\frac{1}{5}\\)
\\(\circ\\) \\(\frac{2}{5}\\)
\\(\circ\\) 2
\\(\circ\\) 5

Explanation:

Step1: Divide y2 by y1

$\frac{\frac{2}{5}}{2} = \frac{2}{5} \times \frac{1}{2} = \frac{1}{5}$

Step2: Verify with next pair

$\frac{\frac{2}{25}}{\frac{2}{5}} = \frac{2}{25} \times \frac{5}{2} = \frac{1}{5}$

Step3: Confirm final pair

$\frac{\frac{2}{125}}{\frac{2}{25}} = \frac{2}{125} \times \frac{25}{2} = \frac{1}{5}$

Answer:

A. $\frac{1}{5}$