Lesson 6

Discover

In this activity you will determine the time when the bacteria reach a certain population using the equation of the laws of logarithms.

Try This 1

Suppose that you begin with a single E. coli bacterium at time 0, and the conditions are appropriate for the bacteria to double in population every 20 min. This growth can be modelled using the equation

1.  
   1. Create a table that shows the number of bacteria at 20-min intervals for 5 h. Your table might start out like this one.

       

      Time (in min)	Number of Bacteria
      0
      20
      40

   2. Use your table to estimate when there would be 10 000 bacteria.
2.  
   1. Follow the steps in the following table to algebraically determine an approximate time when there would be 10 000 bacteria. Make the assumption that the equation can be used to find an approximate time where there would be 10 000 bacteria.
      
      

      Write the equation.
      Substitute the known values for P and P0.
      Take the logarithm of both sides of the equation.
      Use the power law of logarithms, logb (Mn) = n logb M, to “bring down” the exponent
      Divide both sides of the equation by log 2.
      Multiply both sides of the equation by 20.
      Determine a decimal approximation of t.

   2. How does the time you determined in 2.a. compare to your estimate from 1.b.?

Save your responses in your course folder.

Share 1

With a partner or group, discuss the following based on your responses in Try This 1.

1. Explain why the power law of logarithms is necessary to solve many exponential equations.
2. How accurate do you expect the prediction you made in question 2.a. to be? Explain why.

If required, save a summary of your discussion in your course folder.