determining rate of change from a graph\nwhat is the multiplicative rate of change for the exponential…
determining rate of change from a graph\nwhat is the multiplicative rate of change for the exponential function graphed to the left?
Answer
Explanation:
Step1: Recall formula for multiplicative rate
For an exponential function $y = ab^x$, the multiplicative rate of change is $b$. Given two points $(x_1,y_1)$ and $(x_2,y_2)$ on the exponential - function graph, we can use the formula $\frac{y_2}{y_1}=b^{x_2 - x_1}$. Let's take two consecutive points, say $(0,2)$ and $(1,6)$.
Step2: Calculate multiplicative rate
Substitute $x_1 = 0,y_1 = 2,x_2 = 1,y_2 = 6$ into $\frac{y_2}{y_1}=b^{x_2 - x_1}$. We get $\frac{6}{2}=b^{1 - 0}$. Since $\frac{6}{2}=3$ and $b^{1 - 0}=b$, then $b = 3$.
Answer:
3