Question
The function p(x)=500000(0.97)^x models the population of a city, which units on the X access would best display this function
Answers
GPT-4o mini
The function \( p(x) = 500000(0.97)^x \) models the population of a city, where \( x \) typically represents time. Given that this is an exponential decay function (as the population decreases by 3% each time period), the best choice for the units on the x-axis would be years.
Thus, you could label the x-axis as "Years" to represent the passage of time in which the population is declining. This way, the function can effectively illustrate the change in population over time.
Thus, you could label the x-axis as "Years" to represent the passage of time in which the population is declining. This way, the function can effectively illustrate the change in population over time.
Which units on the Y axis would best display this function
GPT-4o mini
The y-axis of the function \( p(x) = 500000(0.97)^x \) represents the population of the city. Therefore, the most suitable unit for the y-axis would be "Population" or simply "Number of People."
You can label the y-axis as "Population" to clearly indicate that the values it represents correspond to the population of the city at different times (as represented by the x-axis in years). This allows the graph to convey the information about the city's population effectively.
You can label the y-axis as "Population" to clearly indicate that the values it represents correspond to the population of the city at different times (as represented by the x-axis in years). This allows the graph to convey the information about the city's population effectively.
Original population or current population
GPT-4o mini
In the context of the function \( p(x) = 500000(0.97)^x \), where \( p(x) \) represents the population at time \( x \):
- The **original population** refers to the population at the starting point of observation (when \( x = 0 \)), which is 500,000 in this function.
- The **current population** refers to the population at any given time \( x \) (post initial measurement) as described by the function.
Since the function calculates the population over time as it decreases, you could refer to the y-axis as **"Current Population"** to emphasize this is the population at each point in time \( x \).
In summary:
- Label the y-axis as "Current Population" to reflect the function's output for the population at different years. If you want to emphasize the starting point, you can mention the **original population** in context, noting it as 500,000 at \( x = 0 \).
- The **original population** refers to the population at the starting point of observation (when \( x = 0 \)), which is 500,000 in this function.
- The **current population** refers to the population at any given time \( x \) (post initial measurement) as described by the function.
Since the function calculates the population over time as it decreases, you could refer to the y-axis as **"Current Population"** to emphasize this is the population at each point in time \( x \).
In summary:
- Label the y-axis as "Current Population" to reflect the function's output for the population at different years. If you want to emphasize the starting point, you can mention the **original population** in context, noting it as 500,000 at \( x = 0 \).