Question

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: 10 this means that the temperature increased 10°f 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: -5 this means the temperature decreased 5°f per hour from 1 p.m. to 2 p.m.

Explanation:

Step1: Recall rate - of - change formula

The rate of change of a quantity (in this case temperature) over an interval is given by $\frac{\text{Change in quantity}}{\text{Change in time}}$.

Step2: Analyze 6 A.M. - 7 A.M.

For the time interval from 6 A.M. to 7 A.M., the rate of change is 10. This means $\frac{\text{Change in temperature}}{\text{1 hour}}=10^{\circ}\text{F/hour}$, so the temperature increased by $10^{\circ}\text{F}$ per hour.

Step3: Analyze 1 P.M. - 2 P.M.

For the time interval from 1 P.M. to 2 P.M., the rate of change is - 5. This means $\frac{\text{Change in temperature}}{\text{1 hour}}=-5^{\circ}\text{F/hour}$, so the temperature decreased by $5^{\circ}\text{F}$ per hour.

Answer:

a. rate of change: 10; This means that the temperature increased $10^{\circ}\text{F}$ per hour from 6 A.M. to 7 A.M.
b. rate of change: - 5; This means the temperature decreased $5^{\circ}\text{F}$ per hour from 1 P.M. to 2 P.M.