Question

The National Weather Service keeps track of the temperature for a given day in a given city. It also keeps track of this information at certain times during a given day. The following temperatures were recorded on a January day in New York City.

Time of Day
10 AM
12 Noon
2 PM
4 PM
6 PM
8 PM
10 PM
Temperature(*F)
30
35
36
36
34
30
28

What is the average rate of change of temperature with respect to time over the evening hours from 6 PM to 10 PM? Interpret this value in a complete sentence.

Answer 1

Looking at the table, can you tell me the temperature at 6 PM ?

Answer 2

34 degrees

Answer 3

Yes, and what is the temperature at 10 PM ?

Answer 4

28 degrees

Answer 5

Whats the change ?

Answer 6

Has it decreased or increased ?

Answer 7

These are the kinds of questions you need to ask yourself to better understand the problem and answer correctly

Answer 8

Decreased by 6

Answer 9

Exactly! How long it took to decrease by 6 degrees ?

Answer 10

4 Hours

Answer 11

6 degrees drop in 4 hours

Answer 12

\[\dfrac{6 ~degrees }{4~ hours} = \dfrac{3}{2} degrees /hour\]

Answer 13

Thank you so much for helping me out!!

Answer 14

Oh wait, we should put a negative sign to show that the temperature is decreasing

Answer 15

Notice the question asks for the average rate of change of temperature,

Not the average temperature

Answer 16

\(\color{red}{-}\dfrac{3}{2}\) degrees per hour is the average change in temperature with respect to time

Answer 17

between 6 PM and 10 PM

Answer 18

I have a similar question and was wondering if you could help me decide whether it is negative or positive.

Answer 19

Sure, ask

Answer 20

Using the same table as the first question, Determine the average rate of change of temperature with respect to time over the entire twelve-hour period given in the table.

The answer I am getting is 0.167 degrees per hour, I'm just not sure if its negative or positive.

Answer 21

Time of Day
10 AM
12 Noon
2 PM
4 PM
6 PM
8 PM
10 PM
Temperature
30
35
36
36
34
30
28

Answer 22

At 10AM, the temperature is 30 degrees
At 10PM, the temperature is 28 degrees

Answer 23

Has the temperature increased or decreased from morning to evening ?

Answer 24

Decreased

Answer 25

so you put a negative sign

Answer 26

The temperature has "decreased" at an average rate of 0.167 degrees per hour.

Answer 27

Equivalently,
The average rate of change in temperature is "-0.167 degrees per hour"

Answer 28

Notice how the negative sign replaces the word "decreased"

Answer 29

Thank you so much for all your help!! I really appreciate it!

Answer 30

Yw!