Question

latasha was tracking the temperature as a weather front was moving into town. the function ( f(x) ) models the total change in temperature, in degrees fahrenheit, after ( x ) hours. as latasha tracked the change, ( f(5)=66 ), ( f(8)=73 ), and ( f(11)=67 ). between hours 5 and 11 of tracking the temperature, what was the average change in temperature per hour? provide an answer accurate to the nearest hundredth.

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) over the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\). Here, \(a = 5\), \(b=11\), \(f(a)=f(5) = 66\), and \(f(b)=f(11)=67\).

Step2: Substitute the values into the formula

Substitute the values into \(\frac{f(b)-f(a)}{b - a}\): \(\frac{67 - 66}{11 - 5}=\frac{1}{6}\approx0.17\)

Answer:

\(0.17\)