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 time since midnight (hours) -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 the time - points

10 am is 10 hours since midnight and noon is 12 hours since midnight.

Step2: Identify the corresponding temperatures

From the graph, at \(x = 10\), \(y\approx60\) degrees F and at \(x = 12\), \(y\approx65\) degrees F.

Step3: 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, \(x_1 = 10,y_1=60,x_2 = 12,y_2 = 65\). So \(\frac{y_2 - y_1}{x_2 - x_1}=\frac{65 - 60}{12 - 10}=\frac{5}{2}=2.5\) degrees F per hour. This means the temperature increased an average of 2.5 degrees per hour.

Answer:

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