Question

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)
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Answer 1

[AI-generated answer — Bot GPT 3.5]

To answer these questions, we can create a table to track the population of Bentonville and Pine Bluff over the years. Let's assume the initial population of Bentonville and Pine Bluff are A and B, respectively.

Year | Bentonville Population | Pine Bluff Population
-----|-----------------------|---------------------
0 | A | B

We need to find the year when the population of Bentonville first exceeds that of Pine Bluff. To determine this, we can create equations for the population growth of both cities.

For Bentonville:
Bentonville Population = A + rB, where r represents the growth rate

For Pine Bluff:
Pine Bluff Population = B + rB

We can set up an equation to find the year when Bentonville's population surpasses Pine Bluff's population:

A + rB = B + rB

Simplifying, we find:

A = B

This equation shows that the population of Bentonville will exceed that of Pine Bluff only when their initial populations are equal. Therefore, the year in which Bentonville's population exceeds Pine Bluff's will be the year when their populations are equal.

Now let's find the year when Bentonville's population is at least twice the size of Pine Bluff's population. We can set up an equation as follows:

A + rB = 2(B + rB)

Simplifying, we find:

A = B

Again, this equation shows that Bentonville's population will be at least twice the size of Pine Bluff's population only when their initial populations are equal. Therefore, the year in which Bentonville's population is at least twice that of Pine Bluff's will be the year when their populations are equal.

To find the specific it will be helpful to have the actual populations of Bentonville and Pine Bluff.