The
amount of work in dropping a whelk to break it open depends on the height of the
drop and the number of times a whelk has to be dropped.
Work = Height * Number of Drops
W = H * N
If you've been working with a data set, the data should automatically be
filled in below. Otherwise, enter your own data or select one of the two other
data sets.
Based on the computed values of work for the individual data points, between what heights is the amount of work the smallest?
The relationship between the height of the drop and the number of drops can be used to investigate the work. Using the method of transforming the data and
using linear regression, the relationship between H and N for the
sample peanut data is:
The equation for the amount of work for the sample peanut data is:
Both
the
expression for the number of drops in terms of the height and the work
in terms of the height are rational expressions. Rational expressions
are those that can
be expressed as the quotient of two polynomials.
Rational expressions can be written in several different forms. Three
common ways of writing a rational expression are show below for the
same rational expression:
Each form of a rational expression provides different information and insight into the nature of the function.
Examine your original work equation and the different ways of
expressing the same expression for N and W.