Interpolation


   

Meet Ursala your kellnerin while you and your 110C classmates are at Oktoberfest in Munich
celebrating your passing of 110C and graduation.  She is new and just learning the ropes and is
spilling some of the Bier.  1L in a Masskruege costs $8 and a half liter bottle costs $5.  You refuse
to pay full price for less than a liter so you complain and she brings the price down to $7.50.
Assuming she priced it correctly, how much beer is left in your Masskruege?

This is a simple interpolation problem.

given:  0.5L      $5
             1L         $8
1.  find out range of beer prices and what fraction of the way down your tab is
     range=8-5=3
     upperbound-tab=8-7.50=0.5
     fraction is 0.5/3=0.1667  or ~17%away from $8   .... or your tab is 100-17=83% of the way to $8
 
2.  Use that fraction to determine how much beer you got
     range=1-0.5=0.5
     amount of beer drank = lowerbound + (range * [1-0.17])
                                         = lowerbound + (range * 0.83) = 0.5L +(0.5L* 0.83) = 0.92L
                                         = upperbound - (range * 0.17) = 1.0L - (0.5L* 0.17) = 0.92 L

3.  Think about your answer, $7.50 is much closer to $8 than $5 so you know that your volume
     of Bier must be closer to 1L than to 0.5L.

-------------------------------------

Now you want to know how fast you can funnel these 0.9L Biers in order to pace yourself.  
After having trained for 4 years in Santa Cruz, you have determined that you can funnel 1L
of american beer (4.2% alchohol) in 10 seconds, a half a liter in 5 seconds, 1L of Colt 45 (8%)
in 20 seconds, and half a liter in 7 seconds.  Assume german beer is 5.5%

                 American beer         German Bier      Colt 45
                          4.6%                        5.5%                  8%

0.5 L                  5 sec                                                 7 sec

0.9L                     ?1                        ?3                           ?2

1L                     10 sec                                               20 sec

Now what?   
1.  Interpolate to find out how fast you can drink 0.9L of american beer = ?1 = 9 sec
2.  Interpolate to find out how fast you can drink 0.9L of Colt 45 = ?2 = 17.4 sec
3.  Interpolate to find out how fast you cand drink 0.9L of german Bier = ?3

 8-4.6 = 3.4
 8-5.5=2.5
 2.5/3.4=0.74
 
 17.4-9=8.4
 8.4*(1-0.74)=2.2
 9+6.2=11.2 seconds!!!!

or

 8.4*0.74=6.2
 17.4-2.9=11.2 seconds!!!

4.  Think about it then order another one.

Note:  Extapolation is what you have to do when, for example, you have 1.1L of beer and want
           to know how long it would take to drink.