Question

the average rate of change from x = 0 to x = 15 is about -14/3. what does this mean in terms of the waterslide, from x = 0 to x = 15? on average, the slide rises 3 feet for every 14 feet of horizontal distance. on average, the slide rises 14/3 feet for every 1 feet of horizontal distance. on average, the slide drops 3 feet for every 14 feet of horizontal distance. on average, the slide drops 14/3 feet for every 1 feet of horizontal distance.

Explanation:

Step1: Understand average rate of change

The average rate of change formula is $\frac{\Delta y}{\Delta x}$. A negative average rate of change means the function (height of waterslide in this case) is decreasing as $x$ (horizontal distance) increases.

Step2: Analyze the value $-\frac{14}{3}$

The negative sign indicates a drop. The value $\frac{14}{3}$ means for every 3 units of horizontal distance ($\Delta x = 3$), the height ($\Delta y$) changes by - 14 units. In other words, for every 1 unit of horizontal distance, the height drops by $\frac{14}{3}$ feet.

Answer:

On average, the slide drops $\frac{14}{3}$ feet for every 1 foot of horizontal distance.