Population Exploration

Name______________________________________________________________________________________

You will be using the data contained in the table on Canadian population census figures from 1851 to 1996 and your TI 83 to answer the following questions.  In total, you should include three graphs* together with this worksheet containing your responses to all questions.  *Use one side of a page of graphing paper and line all three graphs up vertically so that a ruler could be laid vertically along a time period and it would intersect all three graphs at the identical time period.

1.                    How was the total population growth in column three determined?

 

2.                    PAPER AND PENCIL.   Create a graph of the population over time.  Think of a way that you can change the periods into x coordinates and which column of data you would need to use as the y coordinates.

 

A.       Use graph paper to sketch your graph making sure you label axes and use the appropriate units.

 

B.       What type of function is the curve of best fit

 

 

C.      What is the equation of this curve?

 

3.     GRAPHING CALCULATOR. Create another graph of the population growth over time.  (Should this graph be the same or different from the graph in question #2? ) To do this you will want to enter the time periods in L1 and the growth in L2 and use STAT PLOT followed by a regression that you think will be the curve of best fit.

A     Use graph paper to sketch the graph and label the axes appropriately.

 

B.    What type of function is the curve of best fit.  How accurate is the fit?  Is the fit accurate enough to extrapolate out to future periods?

 

C.    What is the equation of this curve?

 

 

4.        Sketch the graph of the function that would approximate the rate of change of the population growth over the time given in the table.  Make sure to label the axes appropriately.

A.    Using other data in the table, what explanations can you give that would explain the nature of the rises and falls in the graph.  Be specific about several periods in which there was a clear change in the rate of growth.

 

B.    When was the rate of growth at a minimum?  A maximum?  What was the reason for this occurrence?

 

D.      Was the population growth ever negative? If your answer is yes then give the time periods below for which it was negative.

 

E.       Discuss the shape of this graph as to it’s highs and lows and where it is increasing and decreasing.  What could you tell the Canadian government about the changes in the rates of population growth? 

 

5.        Wrap up questions:

A.                   Choose one time period and laying a ruler vertically along that time period (*as set forth in the directions for graph construct) discuss the connection between all three graphs at that time.  If you are completing this assignment in a group, every one should use a different time period.

B.                   Write a descriptive paragraph summarizing the population dynamics in Canada over the years 1851 through 1996. 

 

   6.          (Extension)  Analyze any other two sets of data contained in the the table.  Some suggestions include births over time, immigration over time etc.  Do an analysis in much the same way as contained in the assignment questions above.

 

Period

Census population at the end of period

Total  population growth1

Births

Deaths

Immigration

Emigration

 

thousands

1851-1861

3,230

793

1,281

670

352

170

1861-1871

3,689

459

1,370

760

260

410

1871-1881

4,325

636

1,480

790

350

404

1881-1891

4,833

508

1,524

870

680

826

1891-1901

5,371

538

1,548

880

250

380

1901-1911

7,207

1,836

1,925

900

1,550

740

1911-1921

8,788

1,581

2,340

1,070

1,400

1,089

1921-1931

10,377

1,589

2,415

1,055

1,200

970

1931-1941

11,507

1,130

2,294

1,072

149

241

1941-19512

13,648

2,141

3,186

1,214

548

379

1951-1956

16,081

2,433

2,106

633

783

185

1956-1961

18,238

2,157

2,362

687

760

278

1961-1966

20,015

1,777

2,249

731

539

280

1966-19713

21,568

1,553

1,856

766

890

427

1971-1976

23,450

1,882

1,755

824

1,053

358

1976-1981

24,820

1,371

1,820

843

771

278

1981-1986

26,101

1,280

1,872

885

677

278

1986-1991

28,031

1,930

1,933

946

1,199

213

1991-1996

29,672

1,641

1,936

1,024

1,137

229