Question

Which of the contexts below could be modeled by an exponential function?

A. Snow was falling at a rate it 0.75 inches per hour.

B. A music service has a fixer monthly cost and charges $0.75 for each downloaded song.

C. A town’s population grows at a rate of 4.3% every year.

D. An elevator descends at a rate of 11 feet per second.

Answer 1

A town's population that grows at a constant percentage rate can be modeled by an exponential function, which is exemplified in option C.

Step-by-step explanation:

The context that can be modeled by an exponential function is option C: A town’s population grows at a rate of 4.3% every year. This is because exponential growth occurs when the rate of growth, expressed as a percentage, is constant over time. Each year the population grows by a fixed percentage, which compounds over time leading to the characteristic exponential curve.

In contrast, options A, B, and D are not best modeled by an exponential function. Snow falling at a constant rate (A), a fixed service cost with a linear charge per downloaded song (B), and an elevator moving at a constant speed (D) each reflect linear, rather than exponential, characteristics.