the graph shows inches of rain (y) on each of the first 15 days (x) of rainy season in the jungle. find the…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ between $x = x_1$ and $x = x_2$ is $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$. Here, $x_1 = 12$, $x_2=15$.

Step2: Estimate function values from the graph

Let's assume from the graph that at $x = 12$, $y_1=f(12) = 10$ and at $x = 15$, $y_2=f(15)=0$.

Step3: Calculate the average rate of change

Substitute into the formula: $\frac{f(15)-f(12)}{15 - 12}=\frac{0 - 10}{3}=-\frac{10}{3}=-\frac{5}{ \frac{3}{2}}=-\frac{5}{3}\times\frac{2}{1}=-\frac{10}{3}\approx - \frac{5}{3}$ (assuming some approximation in reading the graph values).

Answer:

A. $-\frac{5}{3}$