1. Lesson 1

1.6. Explore 2

Mathematics 30-1 Module 6

Module 6: Exponents and Logarithms

 

You may have noticed from Try This 2 that the graph increases when c > 1. This graph can be used to describe exponential growth.

 

This is a graph of a curve y equals c to the exponent x with c value greater than one. The curve increases with the point (0, 1) indicated.
Source: Pre-Calculus 12.
Whitby, ON: McGraw-Hill Ryerson, 2011.
Reproduced with permission.


When 0 < c < 1, the graph decreases. This graph can be used to describe exponential decay.

 

This is a graph of a curve y equals c to the exponent x with c value greater than zero and less than one. The curve decreases with the point (0, 1) indicated.
Source: Pre-Calculus 12.
Whitby, ON: McGraw-Hill Ryerson, 2011.
Reproduced with permission.

 

The characteristics of all exponential functions of the form y = cx, c > 0, c ≠ 1 are as follows:

  • The domain is {x|x ∈ R}.
  • The range is {y|y > 0, y ∈ R}.
  • There is no x-intercept.
  • The y-intercept is 1.
  • The horizontal asymptote is y = 0.
Self-Check 1

 

textbook

  1. Complete “Your Turn” at the end of “Example 1” on page 338 of the textbook. Answer
  2. Complete question 3 on page 342 of the textbook. Answer
  3. Complete question 6 on page 343 of the textbook. Answer