Question

example
springfield monthly rainfall totals, 2010
in which intervals did the average rate of change
decrease?

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \(y = f(x)\) over the interval \([x_1,x_2]\) is \(\frac{f(x_2)-f(x_1)}{x_2 - x_1}\). If the average rate of change is negative, the function is decreasing over that interval.

Step2: Analyze each interval

• Jan - Feb: \(\frac{1.97 - 0.77}{2 - 1}=\frac{1.2}{1}=1.2>0\) (increasing)
• Feb - Mar: \(\frac{3.94 - 1.97}{3 - 2}=\frac{1.97}{1}=1.97>0\) (increasing)
• Mar - Apr: \(\frac{2.98 - 3.94}{4 - 3}=\frac{- 0.96}{1}=-0.96<0\) (decreasing)
• Apr - May: \(\frac{2.16 - 2.98}{5 - 4}=\frac{-0.82}{1}=-0.82<0\) (decreasing)
• May - June: \(\frac{5.55 - 2.16}{6 - 5}=\frac{3.39}{1}=3.39>0\) (increasing)
• June - July: \(\frac{7.56 - 5.55}{7 - 6}=\frac{2.01}{1}=2.01>0\) (increasing)
• July - Aug: \(\frac{6.92 - 7.56}{8 - 7}=\frac{-0.64}{1}=-0.64<0\) (decreasing)
• Aug - Sept: \(\frac{4.08 - 6.92}{9 - 8}=\frac{-2.84}{1}=-2.84<0\) (decreasing)
• Sept - Oct: \(\frac{1.44 - 4.08}{10 - 9}=\frac{-2.64}{1}=-2.64<0\) (decreasing)

Answer:

Mar - Apr, Apr - May, July - Aug, Aug - Sept, Sept - Oct