Learning Resources

Lesson

In this lesson you will compare the growth of two different bacteria populations. You will be asked to compare the two exponential functions that model both populations, noting how they are different and how they are the same.  You should go to your text book now and read the introduction to Investigation 4 before continuing with the rest of this lesson.

The differences and similarities in the graphs is the main point of the lesson and will be discussed at length in the next section. This investigation just gives a real world example to show the application of these functions.

The time at which the study starts is taken to be time zero, i.e. t = 0.  Bacteria were in the culture and growing before the start of the study. To refer to this time we let t be negative. You should therefore include negative values for t when you draw the axes for your graphs. This is indicated by the domain suggested in the procedure on page 121 of your text.

Note that the number of bacteria in given in thousands. Thus, for example, the number of bacteria present in the first population 3 hours after the study starts is

P = 5³ = 125

This means that there are 125 000 bacteria present in that population at that time.

Also, there were bacteria in the population before the study began. For example, 2 hours before the study began, the number in the first population was:

This means that there were  bacteria present in that population at that time.

You can use your calculator to evaluate the number present at times other than whole numbers of hours. For example, to find the number present in the second population 15 min after the start of the study we would express 15 min as 0.25 h and calculate as follows:

P = 6^0.25 = 1.56508

This means that there are 1.56508 x 1000 or approximately 1565 bacteria present in that population at that time.

Activity

1. Complete Investigation 4 on page121 in your text.
2. Complete Investigation Questions 41 - 49 on page 122.
3. Do the CYU Questions 50 - 52(b), 53 & 54 on page 123.

When you have completed these questions, ask your on-site teacher to get the solutions for you from the Teacher's Resource Binder and check them against your answers. After you do this, if there is something you had trouble with and still do not understand, contact your on-line teacher for help.

Test Yourself

The following exponential function describes the growth of bacteria in a certain culture: , where E(t) is the number of bacteria and t is the time in hours.

1. What was the initial number of bacteria?
2. How many present after 30 min?
3. How many are present after 1 h?
4. How many present after 3 h?

Solution