Pauley graphs the change in temperature of a glass of hot tea over time. He sees that the function appears to decrease quickly at first, then decrease more slowly as time passes. Which best describes this function? It is linear because the graph decreases over time. It is linear because there is both an independent and a dependent variable. It is nonlinear because linear functions are increasing functions. It is nonlinear because linear functions increase or decrease at the same rate.

The function Pauley is observing is nonlinear because it exhibits a changing rate of decrease—starting off steeply and then flattening out over time. This behavior aligns with the concept of cooling, where the rate of heat loss decreases as the temperature of the tea approaches the ambient temperature, creating a curve rather than a straight line. In real-world applications, this scenario can be modeled by Newton's Law of Cooling, which states that the rate of heat loss of an object is proportional to the difference in temperature between the object and its surroundings. By using this model, one can predict how long it will take for the tea to cool to a certain temperature, bringing not just insights into temperature but also delicious beverage timing!