The table shows the temperature in degrees Fahrenheit at different times on a winter day.
Winter Temperatures
Time Temperature ()
2:00 ᴀ.ᴍ. 43
4:00 ᴀ.ᴍ. 46
6:00 ᴀ.ᴍ. 49
8:00 ᴀ.ᴍ. 52
What is the rate of change of the temperature with respect to time?
Option A.
1.5F/h
Option B.
9F/h
Option C.
0.6F/h
Option D.
3F/h
To find the rate of change of temperature with respect to time, we need to calculate the difference in temperature between two time intervals and divide it by the difference in time between those intervals.
First, let's calculate the difference in temperature between 8:00 a.m. and 6:00 a.m.:
Temperature at 8:00 a.m. = 52°F
Temperature at 6:00 a.m. = 49°F
Difference in temperature = 52°F - 49°F = 3°F
Now, let's calculate the difference in time between 8:00 a.m. and 6:00 a.m.:
Time at 8:00 a.m. = 8 hours
Time at 6:00 a.m. = 6 hours
Difference in time = 8 hours - 6 hours = 2 hours
Finally, let's calculate the rate of change:
Rate of change = Difference in temperature / Difference in time
Rate of change = 3°F / 2 hours
Simplifying, we get:
Rate of change = 1.5°F/h
Therefore, the rate of change of the temperature with respect to time is 1.5F/h.
Option A is the correct answer.