The temperature, \( H \), in degrees Celsius, of a hot cup of coffee placed on the kitchen counter is given by \( I I=f(t) \), where \( t \) is in minutes since the coffee was put on the counter. a. Is \( f^{\prime}(t) \) positive or negative? negarive b. What are the units of \( f^{\prime}(20) \) ? degrees Celsiusminute c. Suppose that \( f^{\prime}(20)=-0.1 \) and \( f(20)=75 \). Fill in the blanks and select the appropriate terms to complete the following statement about the temperature of the coffee in this case. d. Suppose that \( f^{\prime}(20)=-0.1 \). Complete the following notation. decreasing - by 0.1 \( d \)

The cooling of coffee is often described using Newton's Law of Cooling, which states that the rate of change of an object's temperature is proportional to the difference between its temperature and the ambient temperature. This means your coffee will cool down faster when it's much hotter than its surroundings! When analyzing temperature changes, it's common to set up experiments measuring how quickly a hot beverage cools over time. Real-world applications can range from everyday kitchen scenarios to industrial processes, like managing the temperature of materials in manufacturing, emphasizing the importance of understanding thermal dynamics in daily life.