Question

algebra: concepts and connections - plc
exponential growth functions
determining rate of change from a graph
what is the multiplicative rate of change for the exponential function shown on the graph?

Explanation:

Step1: Define multiplicative rate

The multiplicative rate of change for an exponential function is the factor \(b\) such that \(b = \frac{y_{n+1}}{y_n}\) for consecutive \(x\)-values.

Step2: Calculate using consecutive points

Take \((0, 2)\) and \((1, 6)\):
\(b = \frac{6}{2} = 3\)

Step3: Verify with other points

Check \((1, 6)\) and \((2, 18)\):
\(b = \frac{18}{6} = 3\)
Check \((-1, \frac{2}{3})\) and \((0, 2)\):
\(b = \frac{2}{\frac{2}{3}} = 3\)

Answer:

3