Learning Resources
Lesson
The introduction to this Focus sets up a situation where the bacteria culture under study starts with one bacterium per square centimetre and increases by a factor of 10 each day. If x represents the days and y represents the number of bacteria, then a table of values can be created as below:
Day |
Number of Bacteria |
0 |
1 |
1 |
10 |
2 |
100 |
3 |
1000 |
4 |
10000 |
... |
... |
The first question in the Focus requires the equation and graph for these values to be found. Recall, it is a simple exponential growth curve and the equation should not be difficult to find.
Using technology, you can determine the number of bacteria present after any number of days or fraction of days as required in question 2. To find the number of days required for any power of 10 number of bacteria can be easily found by solving an exponential equation with a base 10 on each side; however, the values that cannot be expressed as a power of 10 cannot be solved by this method.
Using the TRACE function and/or TABLESET on the TI-83 you can solve the equation as in Section 3.1, lesson 2. Return to that lesson to view the example again.
Question 6 introduces a method that gives an easier way to find the value of x. By entering log 700, on your calculator, the same solution results as you found in question 4. In other words to solve the equation 
you can use the calculator and enter 
In general, then for an exponential equation of the form 
the solution is 
. Make note of this in your notebook since it is essential to the understanding of logarithms.
Activity
Focus Questions p.172. Complete 1, 2, 3, 4, 5 and 6
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.
After you do the assigned activities, continue on to the Test Yourself section below for a quick quiz on this lesson.
Test Yourself
- Solve the following equation by using the TABLE and TABLESET on your TI-83:
- Find log 375 on your calculator. Relate it to your answer from the graph and table.
Click here for suggested solution.