please help

[NIght]

Enrollments in public colleges for recent years are shown in the table. Assuming a linear relationship, estimate the enrollments for a) 2002 and b) 2006. Give answers to the nearest tenth of thousands if applicable.

Year	Enrollment (In Thousands)
2000	11,753
2004	12,980
2008	13,972

This is what i did

(Y₂-Y₁)/(X₂-X₁)= Slope

12,980-11,753/2004-2000 = 1,227/4 = 306.75

Then I did (306.75)(2)+11,753 to get the estimate for 2002 which came out to 12,366.5

did the same for 2006-- (306.75)(2)+12,980=13,593.5

but when I do (306.75)(2)+13,593.5 shouldn't I get 13,972
instead of 14,207?

 

[pappus]

Enrollments in public colleges for recent years are shown in the table. Assuming a linear relationship, estimate the enrollments for a) 2002 and b) 2006. Give answers to the nearest tenth of thousands if applicable.

Year	Enrollment (In Thousands)
2000	11,753
2004	12,980
2008	13,972

This is what i did

(Y₂-Y₁)/(X₂-X₁)= Slope

12,980-11,753/2004-2000 = 1,227/4 = 306.75

Then I did (306.75)(2)+11,753 to get the estimate for 2002 which came out to 12,366.5

did the same for 2006-- (306.75)(2)+12,980=13,593.5

but when I do (306.75)(2)+13,593.5 shouldn't I get 13,972 <--- why? How did you get this value?
instead of 14,207?

By the way I'm very interested to get acquainted to the 0.5 student who was obviously alive in 2006

 

[HallsofIvy]

I'm pretty sure he was in one of my classes.

 

[Deleted member 4993]

By the way I'm very interested to get acquainted to the 0.5 student who was obviously alive in 2006

That's the 10 yr. old that joined college and his brother joined next year.

 

[NIght]

Well According to the table in 2008 the enrollment was 13,972

so after the point (2006, 13593.5) I should get (2008, 13972) right?

but according to the slope that i calculated, (2008, 13972) isn't on the line

 

[stapel]

Well According to the table in 2008 the enrollment was 13,972

so after the point (2006, 13593.5) I should get (2008, 13972) right?

but according to the slope that i calculated, (2008, 13972) isn't on the line

Are you trying to apply the same slope to 2006 (that is, to the midpoint between 2004 and 2008) that you applied to 2002 (that is, to the midpoint between 2000 and 2004)? Perhaps with the different inputs, you should see about getting different outputs.

 

[soroban]

Hello, NIght!

Please check the wording of the problem.
There are two puzzling terms.

Enrollments in public colleges for recent years are shown in the table.
Assuming a linear relationship, estimate the enrollments for a) 2002 and b) 2006.
Give answers to the nearest tenth of thousands if applicable.

. . \(\displaystyle \begin{array}{cc}\text{Year} & \text{Enrollment} \\ \hline 2000 & 11,\!753,\!000 \\ 2004 & 13,\!980,\!000 \\ 2008 & 13,\!972,\!000 \end{array}\)

We do not have a "linear relationship".
The three data-points are not collinear.

The graph looks like this.

      |
      |               o
      |               : 
      |               : 
      |               :
      |       o       :
      |       :       :
      o       :       :
      |       :       :
      |       :       :
  - - + - + - + - + - + - -
      0   2   4   6   8

We might assume a "linear relationship" between each pair of points.
If so, they should have clearly stated that concept.

It's actually a rather silly concept.
Two points always determine a linear relationship.


I assume they are expecting this graph:

      |
      |               o
      |               : 
      |           ♥   : 
      |           :   :
      |       o   :   :
      |   ♥   :   :   :
      o   :   :   :   :
      |   :   :   :   :
      |   :   :   :   :
    - + - + - + - + - + - -
      0   2   4   6   8

Since the intervals are equal,
. . the missing points are the midpoints of the segments.
We need not be concerned with slopes and equations of lines.


I believe that second phrase should be "tens of thousands".