Time interval 6:53 a.m to 8:53 a.m, the average rate of change per hour the greatest.
Given,
Time Temperature (°F)
5:53 a.m. 60.1
6:53 a.m. 60.1
8:53 a.m. 66.9
11:53 a.m 75.2
3:53 p.m. 78.1
From 5:53 a.m. to 6:53 a.m. the temperature is constant. So average rate of change per hour is 0.
From 6:53 a.m to 8:53 a.m. the temperature is increasing from 60.1 to 66.9 or 6.8 in 2 hours . So average rate of change per hour is [tex]\frac{6.8}{2} =3.4[/tex].
From 8:53 a.m. to 11:53 a.m the temperature is again increasing from 66.9 to 75.2 or 8.3 in 3 hours. So average rate of change per hour is [tex]\frac{8.3}{3} =2.76[/tex].
From 11:53 a.m to 3:53 p.m. the temperature is again increasing from 75.2 to 78.1 or 2.9 in 4 hours. So average rate of change per hour is [tex]\frac{2.9}{4}=0.725[/tex].
Now clearly from the above points time interval 6:53 a.m to 8:53 a.m, the average rate of change per hour the greatest.
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