Question

temperature the graph shows the temperature in a city during different hours of one day.

a. find the rate of change in temperature between 6 a.m. and 7 a.m. and describe its meaning in the context of the situation.
rate of change: select choice
this means that the temperature select choice select choice per hour from 6 a.m. to 7 a.m.

b. find the rate of change in temperature from 1 p.m. and 2 p.m. and describe its meaning in the context of the situation.
rate of change: select choice
this means the temperature select choice select choice per hour from 1 p.m. to 2 p.m.

Explanation:

Step1: Recall rate - of - change formula

The rate of change of a function between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Find data points for 6 AM - 7 AM

At 6 AM ($x_1 = 6$), the temperature $y_1=50^{\circ}F$. At 7 AM ($x_2 = 7$), assume the temperature is $y_2 = 60^{\circ}F$ (by visual inspection of the graph). Then the rate of change $\frac{y_2 - y_1}{x_2 - x_1}=\frac{60 - 50}{7 - 6}=10$. This means the temperature is increasing by 10 degrees Fahrenheit per hour from 6 AM to 7 AM.

Step3: Find data points for 1 PM - 2 PM

At 1 PM ($x_1 = 13$), assume the temperature $y_1 = 90^{\circ}F$. At 2 PM ($x_2 = 14$), assume the temperature is $y_2 = 85^{\circ}F$. Then the rate of change $\frac{y_2 - y_1}{x_2 - x_1}=\frac{85 - 90}{14 - 13}=- 5$. This means the temperature is decreasing by 5 degrees Fahrenheit per hour from 1 PM to 2 PM.

Answer:

a. rate of change: 10; This means that the temperature is increasing by 10 degrees per hour from 6 AM to 7 AM.
b. rate of change: - 5; This means the temperature is decreasing by 5 degrees per hour from 1 PM to 2 PM.