Let's suppose that the rain barrel starts with 100 gallons. Then, after 5 minutes, the barrel is left with 89.5 gallons. After 10 minutes, the barrel has 79 gallons. We can find the rate of change with this information:
[tex]\begin{gathered} (x_1,y_1)=(5,89.5) \\ (x_2,y_2)=(10,79) \\ \Rightarrow m=\frac{y_2-y_2}{x_2-x_1}=\frac{79-89.5}{10-5}=\frac{-10.5}{5}=-2.1 \end{gathered}[/tex]therefore, the rate of change is -2.1.
The percentage change from 100 to 89.5 is:
[tex]\begin{gathered} \frac{\text{new value - old value}}{100} \\ \Rightarrow\frac{89.5-100}{100}=-0.105 \end{gathered}[/tex]finally, we have that the percentage change is a decrease of 10.5%
