c. Choose a value for d that is greater than $25 and less than $100. Calculate the
total cost of each of the possible presents for the value you chose. Then write a
short paragraph telling Winona and Takoda which present they should buy and
explaining why.
Question 3
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
n
To calculate the current estimated population of the town, we can use the following expressions:
1) For Pleasantville: x - (0.02)(x) = x - 0.02x = 0.98x
2) For Amity Center: y + (0.05)(y) = y + 0.05y = 1.05y
3) For Harmony Corners: z + (0.07)(z) = z + 0.07z = 1.07z
b. 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.
To add the population information for the town of Concord to the table, we have:
Town | Census Population | Percentage Change
Pleasantville | x | -2%
Amity Center | y | +5%
Harmony Corners | z | +7%
Concord | p | -9%
To calculate the current estimated population of Concord, we can use the following expressions:
1) p - (0.09)(p) = p - 0.09p = 0.91p
2) p + (-0.09)(p) = p - 0.09p = 0.91p
Both expressions show the current estimated population of Concord in terms of p.
i have a question could we use any number like 8
Yes, you can choose any number for p as long as it meets the given criteria of being a negative integer not divisible by two. If you choose 8, for example, you can use the following expressions to calculate the current estimated population of Concord:
1) 8 - (0.09)(8) = 8 - 0.72 = 7.28
2) 8 + (-0.09)(8) = 8 - 0.72 = 7.28
Both expressions show the current estimated population of Concord when p is 8.
no like could it be 0.08
Apologies for the confusion. If you choose 0.08 for p, you can use the following expressions to calculate the current estimated population of Concord:
1) 0.08 - (0.09)(0.08) = 0.08 - 0.0072 = 0.0728
2) 0.08 + (-0.09)(0.08) = 0.08 - 0.0072 = 0.0728
Both expressions show the current estimated population of Concord when p is 0.08.
b. 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
If Concord's population as of the last census was p people and the percentage change is a negative integer not divisible by two, we can add the following row to the table:
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:
1) p - (0.03)(p) = p - 0.03p = 0.97p
2) p + (-0.03)(p) = p - 0.03p = 0.97p
Both expressions show the current estimated population of Concord in terms of p, assuming the negative percentage change is -3%.
c. 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