Question

A cable company with a reputation for poor customer service is losing subscribers at a rate of approximately 3% per year. The company had 2 million subscribers at the start of 2014. Assume that the company continues to lose subscribers at the same rate, and that there are no new subscribers. Which of the following functions, S, models the number of subscribers (in millions) remaining t years after the start of 2014?

A. S(t) = 2,000,000(0.97)^t
B. S(t) = 2,000,000(1.03)^t
C. S(t) = 2,000,000 - 60,000t
D. S(t) = 2,000,000 - 2,000,000t

Answer 1

The correct function to model the declining number of subscribers is S(t) = 2,000,000(0.97)^t, which represents an exponential decay of 3% per year starting with 2 million subscribers.

Step-by-step explanation:

The function that models the number of subscribers remaining t years after the start of 2014 for a cable company losing subscribers at a rate of 3% per year, with no new subscribers being added, is S(t) = 2,000,000(0.97)^t. Option A represents the exponential decay of the subscriber base, where 0.97 is the decay factor corresponding to a 3% loss each year (100% - 3% = 97%). The other functions do not correctly model the situation: Option B represents growth rather than decline, Option C represents a linear decrease, and Option D implies the company loses all subscribers immediately, which is not in line with the given scenario.