Question

svlo algebra 1b - standard (15261)exponential decay functionsthe table represents an exponential function.|$x$|1|2|3|4|| ---- | ---- | ---- | ---- | ---- ||$y$|6|4|$\frac{8}{3}$|$\frac{16}{9}$|what is the multiplicative rate of change of the function?options:0$\frac{1}{3}$$\frac{2}{3}$2

Explanation:

Step1: Define multiplicative rate

The multiplicative rate of change for an exponential function is found by dividing consecutive $y$-values.

Step2: Calculate first ratio

Divide $y(2)$ by $y(1)$:
$\frac{4}{6} = \frac{2}{3}$

Step3: Verify with next ratio

Divide $y(3)$ by $y(2)$:
$\frac{\frac{8}{3}}{4} = \frac{8}{3} \times \frac{1}{4} = \frac{2}{3}$

Step4: Confirm final ratio

Divide $y(4)$ by $y(3)$:
$\frac{\frac{16}{9}}{\frac{8}{3}} = \frac{16}{9} \times \frac{3}{8} = \frac{2}{3}$

Answer:

$\frac{2}{3}$ (matches the bottom-left option)