PASCO Specialty & Mfg. DISCOVER DENSITY SET SE-9719 Manual De Usuario

Discover Density Set

012–07192A

The final equation is thus:

y =   1.47 g/cm

3 

 x

3

,

and replacing the symbols x and y with more meaningful symbols (e for

edge, m for mass), the final result is:

m =  1.47 g/cm

3

  e

3

.

Although this is sometimes a tedious way to discover an equation

representing data, a graph such as that in Figure 4 is a common and effective

way to visually show the relationship.  For this reason it is valuable to

understand the method, even when the existence of technology (such as

Data Studio) provides other methods that are easier to use.

A second method is useful when a relationship such as y = c x

k

 is suspected,

but there is no clue what the exponent might be.  This method is suggested

by taking the logarithm of both sides of the equation:

log(y)   =   log (c x

), and then simplifying,

log(y)   =   log (c)   +   k  log( x)

If we regard  log(y) and log(x) simply as two new variables, and if we

understand that log(c) is merely another constant, we can see that this

equation could be interpreted as just another linear equation.   In this case,  k

is the slope, and  log(c) is the vertical intercept.  Creating a table of the

logarithms of the original data and graphing shows this:  (Again, a

spreadsheet would be helpful.)

-0.1

- 0.1

0.11

+ 0.52

0.30

1.08

0.43

1.47

0.57

1.88