Question

algebra: concepts and connections - plc
exponential growth functions
identifying exponential rate of change
what is the multiplicative rate of change of the exponential function shown on the graph?
options: \\(\frac{9}{2}\\), \\(1\\), \\(\frac{2}{9}\\)

Explanation:

Step1: Recall multiplicative rate rule

For exponential functions, the multiplicative rate of change is $\frac{y_2}{y_1}$ when $x_2 - x_1 = 1$.

Step2: Use adjacent positive x-values

Take $(0,1)$ and $(1,\frac{9}{2})$. Calculate rate:
$\frac{\frac{9}{2}}{1} = \frac{9}{2}$

Step3: Verify with other points

Take $(1,\frac{9}{2})$ and $(2,\frac{81}{4})$. Calculate rate:
$\frac{\frac{81}{4}}{\frac{9}{2}} = \frac{81}{4} \times \frac{2}{9} = \frac{9}{2}$

Answer:

$\frac{9}{2}$