Module 6: Exponents and Logarithms

 


Did You Know?

This is a photo of a tiger swallowtail butterfly sitting on flowers.

iStockphoto/Thinkstock

There are about 130 species of butterflies in Alberta. The species vary in size. The smallest measures about 15 mm, and the largest is over 10 cm from the tips of each wing.



Try This 4

 

There is a logarithmic relationship between butterflies and flowers. In one study, scientists found that the relationship between the number of flower species, F, that a butterfly feeds on and the number of butterflies observed, B, can be modelled by the function F = −2.641 + 8.958 log10 B.

Pre-Calculus 12. Whitby, ON: McGraw-Hill Ryerson, 2011. Reproduced with permission.



  1. Determine algebraically the number of flower species if 100 butterflies are observed.
  2. Determine algebraically the number of butterflies that should be observed if there are 20 flower species.
  3. Use the graph of function F = −2.641 + 8.958 log10 B to check your solution to question 1. Explain why the graph shown in question 2 cannot be used to check your answer for question 2.

     
    This is a graph of the function f of x equals negative 2.641 plus 8.958 log base 10 of B. The graph starts in quadrant 4 and ends in quadrant 1. The x-axis goes from approximately -40 to 100. The y-axis goes from approximately -40 to 40.
  4. Graph, using technology, the function F = −2.641 + 8.958 log10 B to check your answer to question 2. Explain the process you used.
course folder Save your responses in your course folder.

Substitute 20 into the function for F and then solve for B using your knowledge of logarithms.

Substitute 100 into the function for B and then calculate the value.