what is the average rate of change, in hours per day, of the length of eruption from the eruption on january…

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?

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?

Answer

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)