Question

analyzing a situation to determine a relationship

which situation would be best represented by a linear function?

• the temperature of a glass of ice water increases by a factor of 1.05 until it reaches room temperature.
• wind chill temperature decreases at a greater rate for a low wind velocity and decreases at a lower rate for a high wind velocity when the temperature is 10° fahrenheit.
• the outside temperature decreases at a constant rate per hour between sunset and sunrise.
• the body temperature of a person with pneumonia increases rapidly and then decreases as an antibiotic takes effect.

Explanation:

Analyze linear function characteristics

Using the Linear Modeling knowledge point
A linear function is characterized by a constant rate of change (a constant increase or decrease per unit of time).

Evaluate the first option

Using the Linear Modeling knowledge point
An increase "by a factor of 1.05" represents exponential growth, where the value is multiplied by 1.05 at each interval, not a constant additive change.

Evaluate the second option

Using the Linear Modeling knowledge point
A rate of decrease that changes depending on wind velocity indicates a non-constant rate of change, which is non-linear.

Evaluate the third option

Using the Linear Modeling knowledge point
A decrease "at a constant rate per hour" directly defines a constant rate of change, which is the defining characteristic of a linear function.

Evaluate the fourth option

Using the Linear Modeling knowledge point
A temperature that increases rapidly and then decreases has a changing direction and rate, representing a non-linear (possibly quadratic or polynomial) relationship.

Answer:

• The temperature of a glass of ice water increases by a factor of 1.05 until it reaches room temperature.
• Wind chill temperature decreases at a greater rate for a low wind velocity and decreases at a lower rate for a high wind velocity when the temperature is 10° Fahrenheit.
• The outside temperature decreases at a constant rate per hour between sunset and sunrise. (Correct answer)
• The body temperature of a person with pneumonia increases rapidly and then decreases as an antibiotic takes effect.