Hi, I have a question.
Sure, I'm here to help! What would you like to ask?
Oh, it's AI!
A county planner prepares the following table showing population trends in three local
towns. The first column gives the name of the town. The second column gives the
population as of the last census. The third column gives the estimated increase or
decrease in population since that census, expressed as a percentage of the previous
population.
Town Census Population Percentage Change
Pleasantville x –2%
Amity Center y +5%
Harmony Corners z +7%
a. Choose one of these towns. Use the second and third columns to write two
expressions showing the current estimated population of the town in terms of
x, y, or z.
Let's choose the town Pleasantville.
The current estimated population of Pleasantville can be calculated using the second and third columns as follows:
Population of Pleasantville = x + (x * (-2/100))
= x - (0.02x)
= x(1 - 0.02)
= 0.98x
So, the current estimated population of Pleasantville is 0.98x.
Thank you AI!
Add a fourth row to the table showing the population information for the town
of Concord. Concord’s population as of the last census was p people; for its
percentage change, choose a negative integer not divisible by two. Write two
expressions showing the current estimated population of Concord in terms of p.
Sure! I'll add a fourth row to the table and calculate the estimated population of Concord.
Town | Census Population | Percentage Change
---------------------------------------
Pleasantville | x | -2%
Amity Center | y | +5%
Harmony Corners | z | +7%
Concord | p | -3%
To calculate the current estimated population of Concord, we can use the following expressions:
Expression 1:
Population of Concord = p + (p * (-3/100))
= p - (0.03p)
= p(1 - 0.03)
= 0.97p
Expression 2:
Population of Concord = p - abs(p * (-3/100))
= p - abs(0.03p)
= p - 0.03p (since -3/100 is not divisible by 2)
= 0.97p
Therefore, both expressions show that the current estimated population of Concord is 0.97p.
Are there any other easier expressions you could use?
I apologize for any confusion. Yes, there is a simpler expression to represent the current estimated population of Concord in terms of p.
Expression 1:
Population of Concord = p + (p * (-3/100))
= p - (0.03p)
= p(1 - 0.03)
= 0.97p
Expression 2:
Population of Concord = p * (1 - 3/100)
= p * (1 - 0.03)
= p * 0.97
Both expressions represent the current estimated population of Concord as 0.97p.
Choose a number greater than 5,000 and less than 10,000 for the value of p.
Based on the percentage change you chose in part b, calculate the estimated
current population of Concord, rounding to the nearest whole number if
needed. Explain why you used the expression you did to make your calculation.
Let's choose p = 7,500 as the value for Concord's population.
Using the expression Population of Concord = p * 0.97, we can calculate the estimated current population of Concord:
Population of Concord = 7,500 * 0.97
= 7,275
Rounding to the nearest whole number, the estimated current population of Concord is 7,275.
I used the expression Population of Concord = p * 0.97 because the percentage change for Concord was chosen as a negative integer not divisible by two (-3%). This means that the population is decreasing by 3% from the last census. To find the current estimated population, we can subtract 3% of the population from the original population using the expression p * 0.97.
A’Leila is building a pen for her pet donkey. The pen is a rectangle with one side
measuring b yards and the adjacent side measuring a yards. A’Leila knows that
a = 1/3b
.
a. Write two different expressions giving the perimeter of the donkey’s pen.