Problem:
Given the following table of U.S. population:

YearPopulation
(thousands)
17903929
18005308
18107240
18209638
183012861
184017063
185023192
186031443
[Extracted from the Census Bureau WWW site.]

find and graph the exponential model which best approximates the data.


Visualization:
Using the TI-85 graphing calculator:


[Press here to see animation again!]

  1. Press the STAT key and then pick  EDIT  by pressing the F2 key.
  2. You can change the names for the list of values which you will be entering but it is not necessary. Press the ENTER key twice if do not change the names.
  3. To clear out previous data, pick  CLRxy  by pressing the F5 key.
  4. At the prompt  x1= , type in the first year as the first x-value: 1790 and press the ENTER key.
  5. At the prompt  y1= , type in the first population value as the first y-value: 3929 and press the ENTER key.
  6. Keep repeating this to enter all eight pairs of numbers. After you have entered the tenth pair, press the EXIT key.
  7. Pick  CALC  by pressing the F1 key.
  8. Press the ENTER key twice and you will be given the opportunity to choose a number of options including  EXPR  ; choose this option by pressing the F2 key since we want the exponential model.
  9. You will see the following screen:

    This indicates that the equation of the exponential model is:

    y = (4.50164040853 10- 20) (1.02995397837)x

  10. Press the EXIT key followed by the DRAW key.
  11. If some previous graph appears on the screen then
  12. Most probably you will need to change to the bounds of the viewing screen to see all of the data points. To do this,
  13. Pick  SCAT  by pressing the F2 key to see the collection of data points:

  14. Pick  DRREG  by pressing the F4 key to draw the graph of the exponential model: