Question

what is the average rate of change, in hours per day, of the length of eruption from the eruption on january 13 to the eruption on january 18?

Explanation:

Step1: Identify the formula for average rate of change

The formula for average rate of change of a function \(y = f(x)\) over the interval \([x_1,x_2]\) is \(\frac{f(x_2)-f(x_1)}{x_2 - x_1}\). Here, \(x\) represents the number of days after January 11, and \(y\) represents the length of eruption.
For January 13, \(x_1 = 2\) (since \(13 - 11=2\)) and \(y_1 = 6\). For January 18, \(x_2 = 7\) (since \(18 - 11 = 7\)) and \(y_2 = 13\).

Step2: Substitute the values into the formula

Substitute \(x_1 = 2,y_1 = 6,x_2 = 7,y_2 = 13\) into \(\frac{y_2 - y_1}{x_2 - x_1}\).
We get \(\frac{13 - 6}{7 - 2}=\frac{7}{5}=1.4\)

Answer:

\(1.4\)