Why do we use an exponential scale of 100, 10, 1, -1, -10, and -100?
There is no limit to the number of policies that a transportation
provider can implement. Assigning a linear value to policies would result
in a carrier having many policies being rated much more highly or negatively
than carriers that simply ban the transportation of animals.
Policy | Linear Scale | Exponential Scale |
No mammals | 1 | 10 |
No poisonous animals | 1 | 1 |
No wild captured animals | 1 | 1 |
No infected animals | 1 | 1 |
Total Points | 4 | 13 |
No animals accepted | 2 | 100 |
Total Points | 2 | 100 |
Using exponential values in a ratings scale can be beneficial for several reasons:
-
Enhanced Sensitivity to Differences: Exponential scales can
capture and illustrate large differences between values more
effectively than linear scales. This is particularly useful when
the range of values is vast, such as measuring earthquake
magnitudes or sound intensity levels. A small increase in the
rating reflects a significant real-world difference, making it
easier to distinguish between high values.
https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_I_(2211)/02%3A_Vectors/2.07%3A_Math_Review_of_Other_Topics/2.7.14%3A_Exponential_and_Logarithmic_Functions
https://math.libretexts.org/Bookshelves/Applied_Mathematics/Developmental_Math_(NROC)/18%3A_Exponential_and_Logarithmic_Functions/18.04%3A_New_Page/18.4.2%3A_Mathematical_Modeling_with_Exponential_and_Logarithmic_Functions -
Perception Alignment: Human perception of various phenomena,
such as sound and light intensity, tends to be logarithmic.
Exponential scales align better with how we perceive changes,
making the ratings more intuitive and meaningful. For example,
the Richter scale for earthquakes and the decibel scale for
sound both use logarithmic principles to correspond to our
perception of intensity.
https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_I_(2211)/02%3A_Vectors/2.07%3A_Math_Review_of_Other_Topics/2.7.14%3A_Exponential_and_Logarithmic_Functions
https://math.libretexts.org/Bookshelves/Applied_Mathematics/Developmental_Math_(NROC)/18%3A_Exponential_and_Logarithmic_Functions/18.04%3A_New_Page/18.4.2%3A_Mathematical_Modeling_with_Exponential_and_Logarithmic_Functions -
Data Visualization: Exponential scales can improve the
visualization of data, making it easier to spot trends and
patterns. When plotting data that grows exponentially, a
logarithmic scale can turn a steep curve into a straight line,
simplifying analysis and interpretation.
https://courses.lumenlearning.com/ccbcmd-math-1/chapter/graphs-of-exponential-and-logarithmic-functions/