1. Lesson 1

1.10. Explore 6

Mathematics 30-1 Module 6

Module 6: Exponents and Logarithms

 

textbook

Read “Example 1” on page 349 of the textbook. Notice how, in the example, each point is transformed first by the vertical stretch and then by the horizontal translation using a table.

 

Self-Check 3
  1. Complete “Your Turn” at the end of “Example 1” on page 351 of the textbook. Answer
  2. Complete question 8 on page 367 of the textbook. Answer
  3. Complete questions 1 to 5 in “Exponential Functions – Activity B.”

     
    This is a play button that opens Exponential Functions - Activity B.
    Screenshot reprinted with permission of ExploreLearning

You have graphed a given function using transformations. Can you write a function if given a graph? In Try This 5 you will look at an example of how bacteria growth can be modelled using an exponential function.

 

Try This 5

 

This is a picture of a scientist looking at a sample of bacteria.

Wavebreak Media/Thinkstock

A scientist grew a type of bacteria in a Petri dish and started with 300 bacteria. The scientist found that the bacteria increased in population at an exponential rate of 60% every 4 d.

 

Answer the following questions to determine the exponential function for this situation in the form P = a(c)bt, where the population, P, is a function of the bacteria over time, t, in days. A graph of this situation is shown.

 

This is a graph of exponential increase of a population of bacteria over time in days. The points (0, 300) and (4, 480) are indicated on the graph.

  1. Is the value of c > 1 or is 0 < c < 1?
  2. Determine the c-value. Explain your answer.
  3. Determine the b-value. Explain your answer.
  4. Determine the a-value. Explain your answer.
  5. Write the equation that models the growth of this bacteria in the form P = a(c)bt, where P is the population and t is the time in days.

course folder Save your responses in your course folder.

The initial amount of bacteria is 300, so the y-intercept is at 300.
Instead of a 60% increase each day, the increase happens over 4 d.
The value of c depends on the rate of increase or decrease; in this case, the bacteria is increasing at 60% every 4 d. A decrease of 60% would be shown by a c-value of 0.6. How would an increase of 60% be represented by c?
If the graph is increasing, then c > 1. If the graph is decreasing, then 0 < c < 1.