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.”
   
   
    
   
   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

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.

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.

Save your responses in your course folder.