Question

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.

Explanation:

Step1: Recall linear function properties

Linear functions have a constant rate of change (slope), meaning they increase or decrease at the same rate.

Step2: Analyze the tea temperature function

The tea's temperature decreases quickly first, then more slowly. This means the rate of decrease is not constant.

Step3: Evaluate each option

• First option: Linear functions need constant rate, not just decreasing. Eliminate.
• Second option: Having independent/dependent variables doesn't make it linear. Eliminate.
• Third option: Linear functions can decrease (e.g., \( y = -x \)). Eliminate.
• Fourth option: Matches the analysis (nonlinear because linear has constant rate).

Answer:

D. It is nonlinear because linear functions increase or decrease at the same rate.