Question

1. which scenario is best modeled by a linear function?

a. the total cost of bananas per pound.
b. the growth of bacteria in a petri dish.
c. the depreciation of a car over time.
d. the decrease in temperature as time passes during the night.

Explanation:

A linear function has a constant rate of change.

• Option a: Total cost of bananas per pound follows $C = kp$ where $C$ is total cost, $k$ is cost per pound, $p$ is pounds. This is a proportional linear function with a constant rate (cost per pound).
• Option b: Bacteria growth is exponential, not linear, as it multiplies over time.
• Option c: Car depreciation is often exponential or follows a non-linear declining model, not a constant rate.
• Option d: Nighttime temperature decrease is not constant; it may slow or speed up based on environmental factors, so it is non-linear.

Answer:

a. The total cost of bananas per pound.