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The number of movie rental stores in the country has declined exponentially since 2008, as shown in the graph below. Let x repr...Question
The number of movie rental stores in the country has declined exponentially since 2008, as shown in the graph attached. 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 based on the graph attached?
A. All rational numbers 0 to 100
B. all positive real numbers
C. all whole numbers 0 to 9,000
D. All integers
A. All rational numbers 0 to 100
B. all positive real numbers
C. all whole numbers 0 to 9,000
D. All integers
Answers
Answered by
GPT-4o mini
To determine the domain of the function that represents the number of movie rental stores as a function of time in years after 2008, we need to consider what x (time in years) can represent in this context.
Since x starts from 0 (which represents the year 2008) and goes onward in time, the domain will typically include non-negative values. However, the number of movie rental stores (y) cannot be negative, and we would expect that as time progresses, the count of rental stores may continue to decline.
Given the options provided:
A. **All rational numbers 0 to 100** - This option suggests fractional values and is too specific in range.
B. **All positive real numbers** - This implies values of x starting just above 0, and does not include 0 itself.
C. **All whole numbers 0 to 9,000** - This defines a specific range and would not accurately capture any possible future years beyond 9,000.
D. **All integers** - This would imply any integer value, including negative, which is irrelevant in this context.
Considering these options, the most appropriate answer would be:
**C. all whole numbers 0 to 9,000.**
This option implies that we are considering a range of whole years starting from 0 (2008) without going into specific values arbitrarily, and it correctly captures the years without negatives or fractions.
Since x starts from 0 (which represents the year 2008) and goes onward in time, the domain will typically include non-negative values. However, the number of movie rental stores (y) cannot be negative, and we would expect that as time progresses, the count of rental stores may continue to decline.
Given the options provided:
A. **All rational numbers 0 to 100** - This option suggests fractional values and is too specific in range.
B. **All positive real numbers** - This implies values of x starting just above 0, and does not include 0 itself.
C. **All whole numbers 0 to 9,000** - This defines a specific range and would not accurately capture any possible future years beyond 9,000.
D. **All integers** - This would imply any integer value, including negative, which is irrelevant in this context.
Considering these options, the most appropriate answer would be:
**C. all whole numbers 0 to 9,000.**
This option implies that we are considering a range of whole years starting from 0 (2008) without going into specific values arbitrarily, and it correctly captures the years without negatives or fractions.