The average rate of change can be found by dividing the change in temperature by the change in time.
B
b
The average rate of change can be found by dividing the change in temperature by the change in time.
C
c
Find the average rate of change in Lisa's temperature for each 12-hour period.
A
a
Average Rate of Change: 0.15^(∘) per hour
B
b
Average Rate of Change: -0.125 per hour
Explanation: Reasonable, see solution.
C
c
8:00AM on Monday to 8:00PM on Monday
Practice makes perfect
a
We have been given a table that shows Lisa's temperature during an illness over 3-day period.
Monday
Tuesday
Wednesday
Time
8:00AM
8:00PM
8:00AM
8:00PM
8:00AM
8:00PM
Temp (^(∘)F)
100.5
102.3
103.1
100.7
99.9
98.6
To find the average rate of change in Lisa's temperature, we will use a formula.
average rate of change&=change in y/change in x [1.2em]
&=change in temperature/change in time
To find the change in time, it may be helpful to write the time in the 24-hour format.
Monday
Tuesday
Wednesday
Time
8:00
20:00
8:00
20:00
8:00
20:00
Temp (^(∘)F)
100.5
102.3
103.1
100.7
99.9
98.6
Now we can find the change in temperature and time.
change in temperature:& 102.3- 100.5= 1.8
change in time:& 20- 8= 12
Next, we can calculate the average rate of change.
average rate of change&=1.8/12=0.15
The average rate of change in Lisa’s temperature is 0.15^(∘) per hour.
b
From 8:00AM on Tuesday to 8:00PM on Wednesday, there are 36 hours. Next, we will determine the change in temperature.
change in temperature:& 98.6- 103.1= -4.5
change in time:& 36
Now we can find the average rate of change.
average rate of change&=-4.5/36=-0.125
The average rate of change from 8:00AM on Tuesday to 8:00PM on Wednesday is -0.125^(∘) per hour. The answer is reasonable. The number should be negative because her temperature is dropping.
c
Let's find the average rate of change in Lisa's temperature for each 12-hour period.
12-hour Period
Average Rate of Change
8:00AM on Monday-8:00PM on Monday
102.3- 100.5/12=1.8/12=0.15
8:00PM on Monday-8:00AM on Tuesday
103.1- 102.3/12=0.8/12=0.7
8:00AM on Tuesday-8:00PM on Tuesday
100.7- 103.1/12=-2.4/12=-0.2
8:00PM on Tuesday-8:00AM on Wednesday
99.9- 100.7/12=-0.8/12=-0.07
8:00AM on Wednesday-8:00PM on Wednesday
98.6- 99.9/12=-1.3/12=-0.11
The average rate of change in Lisa’s temperature was greatest during 8:00AM on Monday to 8:00PM on Monday.
