During what year will the population of Bentonville first exceed that of Pine Bluff?
During what year will the population of Bentonville be at least twice the size of the population of Pine Bluff?
Show all of your work and explain your steps.
To find this information you may use a graphing calculator such as Desmos to plot both lines and upload a screenshot of the graph showing the answers to these questions. Alternatively, you may create a table and find the populations for different years and find the answers that way.
(4 points)
To find the answers to these questions, we can create a table and find the populations for different years.
Let's assume the current population of Bentonville is 50,000 and the current population of Pine Bluff is 75,000.
Year Bentonville Pine Bluff
--------------------------------
2020 50,000 75,000
2021 55,000 77,000
2022 60,000 80,000
2023 65,000 82,000
2024 70,000 85,000
2025 75,000 88,000
... ... ...
... ... ...
We can observe that the population of Bentonville is increasing at a faster rate than the population of Pine Bluff. By continuously adding some consistent number to the population of Bentonville and a smaller consistent number to the population of Pine Bluff, we will eventually reach the point where the population of Bentonville exceeds that of Pine Bluff and where the population of Bentonville is at least twice the size of the population of Pine Bluff.
To determine the exact year, we can continue this process until these conditions are met. Let's assume we continue adding 5,000 to the population of Bentonville and 2,000 to the population of Pine Bluff each year.
2020 50,000 75,000
2021 55,000 77,000
2022 60,000 80,000
2023 65,000 82,000
2024 70,000 85,000
2025 75,000 88,000
2026 80,000 90,000
2027 85,000 92,000
2028 90,000 94,000
2029 95,000 96,000
2030 100,000 98,000
From the table, we can see that in the year 2030, the population of Bentonville (100,000) exceeds that of Pine Bluff (98,000) for the first time.
To find the year when the population of Bentonville is at least twice the size of Pine Bluff, we continue adding values and updating the table.
2031 105,000 100,000
In the year 2031, the population of Bentonville (105,000) is at least twice the size of Pine Bluff (100,000). Therefore, the year when the population of Bentonville will be at least twice the size of Pine Bluff is 2031.
Note: The given values and growth rates are assumptions for illustrative purposes. The actual values and growth rates can vary.
what the answer
Based on the calculations and assumptions provided, the answer is:
- The population of Bentonville will first exceed the population of Pine Bluff in the year 2030.
- The population of Bentonville will be at least twice the size of the population of Pine Bluff in the year 2031.