Question

the table represents an exponential function.

x	y
2	4
3	\\(\frac{8}{3}\\)
4	\\(\frac{16}{9}\\)

what is the multiplicative rate of change of the function?
\\(\frac{1}{3}\\)
\\(\frac{2}{3}\\)
2
9

Explanation:

Step1: Divide y2 by y1

$\frac{4}{6} = \frac{2}{3}$

Step2: Verify with next y values

$\frac{\frac{8}{3}}{4} = \frac{8}{3} \times \frac{1}{4} = \frac{2}{3}$

Step3: Confirm with last pair

$\frac{\frac{16}{9}}{\frac{8}{3}} = \frac{16}{9} \times \frac{3}{8} = \frac{2}{3}$

Answer:

$\frac{2}{3}$ (Option: $\boldsymbol{\frac{2}{3}}$)