Question
The population of birds in a nearby area is decreasing. The function f (x) = 175(0.755)* represents the population of the birds x years
after the number of birds is first measured. The graph models the function.
200
Population of Birds
: 150
100
50
1
2 3 4 5 6 7
Time (in years)
8
- *
9 10
What is the most reasonable domain for the graph of the function?0≤ x ≤ 200
B 225 x ≤ 200
C x20
D x≤ 10
after the number of birds is first measured. The graph models the function.
200
Population of Birds
: 150
100
50
1
2 3 4 5 6 7
Time (in years)
8
- *
9 10
What is the most reasonable domain for the graph of the function?0≤ x ≤ 200
B 225 x ≤ 200
C x20
D x≤ 10
Answers
GPT-4o mini
To determine the most reasonable domain for the function \( f(x) = 175(0.755)^x \), we need to consider the context of the problem. The function models the population of birds \( x \) years after the measurement begins.
1. The variable \( x \) represents time in years, which cannot be negative. Therefore, it makes sense for \( x \) to be \( 0 \) or greater. This rules out options that include negative values for \( x \).
2. The function represents the population of birds and could be evaluated over the years for practical purposes. Realistically, the population is unlikely to be measured over an extremely long time period given that bird populations can stabilize or shift significantly due to ecological factors.
3. Given that we see the population is decreasing in a graph, the typical lifespan of such measurements might be considered a decade or slightly longer, depending on the specifics of the environment.
Considering these points, the most reasonable domain from the provided options would be:
- **D: \( x \leq 10 \)**
This option implies that the function is evaluated from the start (year 0) up to 10 years. Therefore, it is the most reasonable choice for the domain of this function regarding bird population measurement.
1. The variable \( x \) represents time in years, which cannot be negative. Therefore, it makes sense for \( x \) to be \( 0 \) or greater. This rules out options that include negative values for \( x \).
2. The function represents the population of birds and could be evaluated over the years for practical purposes. Realistically, the population is unlikely to be measured over an extremely long time period given that bird populations can stabilize or shift significantly due to ecological factors.
3. Given that we see the population is decreasing in a graph, the typical lifespan of such measurements might be considered a decade or slightly longer, depending on the specifics of the environment.
Considering these points, the most reasonable domain from the provided options would be:
- **D: \( x \leq 10 \)**
This option implies that the function is evaluated from the start (year 0) up to 10 years. Therefore, it is the most reasonable choice for the domain of this function regarding bird population measurement.