Question:
The most freakish change in temperature ever recorded was from \(-4^\circ\)F to \(45^\circ\)F between 7:30am and 7:32am on January 22, 1943 in Spearfish, SD. What was the rate of change of the temperature for this time period?
Solution:
Rate of Change = \(\frac{\mbox{Change in Output}}{\mbox{Change in Input}} \)
\( T= \) Temperature in degrees Fahrenheit
\( t = \) time in minutes
It is natural to think of temperature as being a function of time. That is to say \( T= f(t) \).
In other words,
\(T\) is output
\( t \) is input
Rate of Change \( = \frac{\Delta T}{\Delta t} = \frac{45-(-4)}{32-30} = \frac{49}{2} = 24.5 \mbox{F}^\circ/\mbox{min} \)
