A COUNTRY 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.
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 DIVISBLE BY TWO. WRITE TWO EXPRESSIONS SHOWING THE CURRENT ESTIMATED POPULATION OF CONCORD IN TERMS OF P.
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 EXPRESSIONS YOU DID TO MAKE YOUR CALCULATION.
A. Let's choose the town of Pleasantville. We can use the second and third columns to write two expressions showing the current estimated population of Pleasantville in terms of X.
Expression 1: X - 0.02X = X(1 - 0.02) = 0.98X (Since the percentage change is -2%, we subtract 2% or 0.02 from the previous population X.)
Expression 2: X(1 - 2%) = X(1 - 0.02) = 0.98X (This is another way to express the decrease of 2% from the previous population X.)
B. Let's add a fourth row to the table for the town of Concord.
TOWN CENSUS POPULATION PERCENTAGE CHANGE
PLEASANTVILLE X -2%
AMITY CENTER Y +5%
HARMONY CORNERS Z +7%
CONCORD P -3%
We choose a negative integer not divisible by two, -3%, for the percentage change of Concord. Now let's write two expressions showing the current estimated population of Concord in terms of P.
Expression 1: P - 0.03P = P(1 - 0.03) = 0.97P (Since the percentage change is -3%, we subtract 3% or 0.03 from the previous population P.)
Expression 2: P(1 - 3%) = P(1 - 0.03) = 0.97P (This is another way to express the decrease of 3% from the previous population P.)
C. Let's choose P = 7,000 for the value of P. Based on the percentage change of -3% from part B, we can calculate the estimated current population of Concord.
Estimated current population of Concord = 7,000 - 0.03(7,000) = 7,000 - 210 = 6,790 (rounded to the nearest whole number)
We used the expressions 7,000 - 0.03(7,000) and 7,000(1 - 3%) to make the calculation because they represent the decrease of 3% from the previous population of 7,000. The expressions allow us to subtract the percentage decrease from the previous population to get the estimated current population.