Question

volume (cubic feet) time (seconds) which statement describes the rate of change for this situation a the volume of the water increases 20 cubic feet per second. b the volume of the water increases 15 cubic feet per second. c the volume of the water increases 30 cubic feet per second. d the volume of the water increases 10 cubic feet per second.

Explanation:

Step1: Identify slope formula

The rate of change is the slope, calculated as $\text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$

Step2: Pick points from the graph

Use $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(6,90)$

Step3: Calculate the rate of change

$\text{Rate of change} = \frac{90 - 0}{6 - 0} = 15$

Answer:

B. The volume of the water increases 15 cubic feet per second.