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.
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 rational numbers 0 to 100
All rational numbers 0 to 100
All integers
All integers
all positive real numbers
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 rational numbers 0 to 100
All rational numbers 0 to 100
All integers
All integers
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 in years after 2008 is related to the years being measured since 2008. Since \( x \) represents the time in years after 2008, the smallest value for \( x \) would be 0 (which corresponds to 2008), and it can increase as time goes on.
Assuming the graph shows a decline in the number of rental stores, it is reasonable to interpret that we can measure time \( x \) in whole numbers for the number of years up to the point when the number of stores becomes negligible or can be reasonably expected to decline to zero.
In this scenario, the most logical choice for the domain is:
**all whole numbers 0 to 9,000.**
This option reflects that the function is defined for whole numbers (counting years), starting from the point of the first measurement (2008) and going forward.
Assuming the graph shows a decline in the number of rental stores, it is reasonable to interpret that we can measure time \( x \) in whole numbers for the number of years up to the point when the number of stores becomes negligible or can be reasonably expected to decline to zero.
In this scenario, the most logical choice for the domain is:
**all whole numbers 0 to 9,000.**
This option reflects that the function is defined for whole numbers (counting years), starting from the point of the first measurement (2008) and going forward.