Question
The number of movie rental stores in the country has declined exponentially since 2008, as shown in the graph below. Let x represent the time, in years after 2008, and y represent the number of movie rental stores.
the line moves In a curved path
(0,9000) (10,3000)
What is the domain of the function that represents the number of movie rental stores as a function of time in years after 2008?
(1 point)
Responses
all whole numbers 0 to 9,000
all whole numbers 0 to 9,000
All integers
All integers
All rational numbers 0 to 100
All rational numbers 0 to 100
all positive real numbers
the line moves In a curved path
(0,9000) (10,3000)
What is the domain of the function that represents the number of movie rental stores as a function of time in years after 2008?
(1 point)
Responses
all whole numbers 0 to 9,000
all whole numbers 0 to 9,000
All integers
All integers
All rational numbers 0 to 100
All rational numbers 0 to 100
all positive real numbers
Answers
Answered by
GPT-4o mini
The domain of the function that represents the number of movie rental stores as a function of time (x, in years after 2008) refers to the possible values of \( x \) (the time in years) for which the function is defined.
Based on the context provided, it appears that the function is defined for \( x \) starting from 0 (2008) and increasing. It is reasonable to assume that this data is limited to the span of time from 2008 until a point when there are no longer any movie rental stores.
Since you presented points for \( x \) ranging from 0 to 10, it suggests examining the situation over a given time period (in this instance, from 2008 until 2018).
Thus, the reasonable interpretation of the domain for \( x \) is:
- **0 to 10**: This implies that years are being measured from 0 in 2008 to 10 in 2018, representing a finite duration.
With that in mind, none of the listed responses perfectly fits the domain explanation. However, the most appropriate choice aligns with:
- **All whole numbers from 0 to 10.**
If focusing strictly on the listed responses, we can't select "all positive real numbers" or "all integers" since these include values outside the practical timeline.
Thus, if we must choose from the options given without the specific nominal wording I suggested, consider the context to imply the limitation likely means choosing a bounded interval.
Based on the context provided, it appears that the function is defined for \( x \) starting from 0 (2008) and increasing. It is reasonable to assume that this data is limited to the span of time from 2008 until a point when there are no longer any movie rental stores.
Since you presented points for \( x \) ranging from 0 to 10, it suggests examining the situation over a given time period (in this instance, from 2008 until 2018).
Thus, the reasonable interpretation of the domain for \( x \) is:
- **0 to 10**: This implies that years are being measured from 0 in 2008 to 10 in 2018, representing a finite duration.
With that in mind, none of the listed responses perfectly fits the domain explanation. However, the most appropriate choice aligns with:
- **All whole numbers from 0 to 10.**
If focusing strictly on the listed responses, we can't select "all positive real numbers" or "all integers" since these include values outside the practical timeline.
Thus, if we must choose from the options given without the specific nominal wording I suggested, consider the context to imply the limitation likely means choosing a bounded interval.