Question

According to a trend, the number of viewers of a popular TV show declines every week. Assuming the show will be aired for a considerable period of time, the approximate number of viewers, in millions, t months after the show was first aired, is shown by the following expression: 5.84(0.96)4t Which statement below best describes the base, 0.96?

A) The number of times the number of viewers declined since the show was first aired.

B) The number of viewers when the show was first aired.

C) The weekly decrease in the number of viewers.

D) The rate at which the number of viewers declines

Answer 1

The base, 0.96, in the expression 5.84(0.96)⁴ᵗ represents the rate at which the number of viewers declines.

Step-by-step explanation:

In the given expression, 5.84(0.96)⁴ᵗ, the base, 0.96, is the factor by which the number of viewers declines each week. This is evident from the exponent of 4, indicating that the decline occurs over a span of 4 weeks. Therefore, option (D) "The rate at which the number of viewers declines" best describes the role of the base in the expression.

Options (A), (B), and (C) do not accurately represent the significance of the base. Option (A) refers to the number of times the viewers declined, which is not the case here. Option (B) suggests the number of viewers when the show was first aired, and option (C) implies the weekly decrease, which are not accurate interpretations of the base in the given context.

Understanding the role of the base in an exponential expression is crucial for interpreting trends and predictions in various scenarios, including the decline in viewership over time in this particular TV show. The base is a key factor that determines the rate of change or decay in such mathematical models.