Module 6: Exponents and Logarithms

 

In Try This 3 you may have determined that the function that modelled the amount of Iodine-131, A, and time, t, in 8-d intervals was . The function A = 2−t could also be used, since .

 

The base is one-half because the amount of Iodine-131 is decreasing by half over each 8-d interval. The domain of the function is {t|t ≥ 0, t ∈ R}, and the range is {A|0 < A ≤ 1, A ∈ R}. You may have determined that it would take 4 eight-day intervals, or 32 d, for 0.0625 g of Iodine-131 to be left.

 

View Determining an Exponential Function to see an example of how to determine the equation of an exponential growth function from its graph.

 

 

This is a play button that opens Determining an Exponential Function.

 

Self-Check 2

 

textbook

  1. Complete “Your Turn” at the end of “Example 3” on page 341 of the textbook. Answer
  2. Complete question 11 on page 344 of the textbook. Answer
 
Try This 4

 

Open Multiple Transformations. Click on the boxes to deselect Quadratic and select Exponential.

 

 

This is a play button that opens Multiple Transformations.

  1. Use the sliders to increase and decrease the a, b, h, and k values. Describe how the parameters a, b, h, and k in the form f(x) = a(c)b(x–h) + k transform the graph. Complete a table like the one shown.

    Parameter

    Describe Effect on Graph

    a

     

    b

     

    h

     

    k

     
  2. How do your responses compare to your knowledge of transformations from past lessons?

course folder Save your responses in your course folder.