Question

a citys temperature at various times on a given day is shown in the graph. find the rate of change of the function between 10 am and noon and describe its meaning in the context of the situation.
todays weather
-3 1/3 degrees f per hour, the temperature decreased an average of 3 1/3 degrees per hour.
2.5 degrees f per hour. the temperature increased an average of 2.5 degrees per hour.
1 degrees f per hour. the temperature increased an average of 1 degrees per hour.
-2.5 degrees f per hour. the temperature decreased an average of 2.5 degrees per hour.

Explanation:

Step1: Identify time - points and temperatures

10 am is 10 hours since midnight, noon is 12 hours since midnight. From the graph, at \(x = 10\), \(y_1\approx60\) and at \(x = 12\), \(y_2\approx65\).

Step2: Calculate the rate of change

The rate - of - change formula is \(\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1}\). Here, \(x_1 = 10\), \(x_2 = 12\), \(y_1\approx60\), \(y_2\approx65\). So \(\frac{y_2 - y_1}{x_2 - x_1}=\frac{65 - 60}{12 - 10}=\frac{5}{2}=2.5\).

Answer:

2.5 degrees F per hour. The temperature increased an average of 2.5 degrees per hour.