Crystal Violet Math Extensions

I. You currently have a linear regression model y=ax+b where y is actually equal to ln A , with A representing the absorbance of the solution. Substitute ln A in for Y and solve for A:

A. Now determine the absorbance after:

  1. 100 seconds:
  2. One minute:


B. How long will the reaction need to run to generate an absorbance of:

  1. .25
  2. .125


C. What is the y intercept of this equation and what is its significance?



II. You have previously determined the half-life of this reaction. Use that number to write a base 1/2 exponential equation which expresses absorbance in terms of time (your answer to C above may also prove helpful):

A. Use your calculator to show that this equation and the base e equation from part I are graphically equivalent:



B. Use your exponential and log properties to algebraically prove that these two are equivalent: