Question

1. the table shows the amount of water in a pitcher at different times. graph the data and show the rates of change. between which two hours is the rate of change the greatest?

time (h)	0	1	2	3	4	5	6	7

Explanation:

Step1: Recall rate - of - change formula

The rate of change between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Calculate rate of change between 0 and 1 hours

Let $(x_1,y_1)=(0,60)$ and $(x_2,y_2)=(1,50)$. Rate of change $=\frac{50 - 60}{1-0}=\frac{- 10}{1}=-10$.

Step3: Calculate rate of change between 1 and 2 hours

Let $(x_1,y_1)=(1,50)$ and $(x_2,y_2)=(2,25)$. Rate of change $=\frac{25 - 50}{2 - 1}=\frac{-25}{1}=-25$.

Step4: Calculate rate of change between 2 and 3 hours

Let $(x_1,y_1)=(2,25)$ and $(x_2,y_2)=(3,80)$. Rate of change $=\frac{80 - 25}{3 - 2}=\frac{55}{1}=55$.

Step5: Calculate rate of change between 3 and 4 hours

Let $(x_1,y_1)=(3,80)$ and $(x_2,y_2)=(4,65)$. Rate of change $=\frac{65 - 80}{4 - 3}=\frac{-15}{1}=-15$.

Step6: Calculate rate of change between 4 and 5 hours

Let $(x_1,y_1)=(4,65)$ and $(x_2,y_2)=(5,65)$. Rate of change $=\frac{65 - 65}{5 - 4}=\frac{0}{1}=0$.

Step7: Calculate rate of change between 5 and 6 hours

Let $(x_1,y_1)=(5,65)$ and $(x_2,y_2)=(6,65)$. Rate of change $=\frac{65 - 65}{6 - 5}=\frac{0}{1}=0$.

Step8: Calculate rate of change between 6 and 7 hours

Let $(x_1,y_1)=(6,65)$ and $(x_2,y_2)=(7,50)$. Rate of change $=\frac{50 - 65}{7 - 6}=\frac{-15}{1}=-15$.

Answer:

Between 2 and 3 hours