Learning Resources

Lesson

Focus J deals with applying the laws of exponents and the laws of logarithms to various problem solving situations. There are no new concepts in this lesson. It provides a chance for you to hone your skills with exponents and logarithms by doing more problems.

Some examples of the type of problems you are asked to do in the text are provided in this lesson as a model for you to follow. As you go through each interactive demo, write the problem on your notebook and try to complete the next step yourself before you click to advance.

Example 1

Solve for x the equation: 

Solution

Remember, write the problem in your note book and try the first step yourself before you advance to the next frame in the interactive.

Example 2

Solve for x: 

Solution

Example 3

Solve for x the equation: 

Solution

Example 4

Vivian is testing a new antiseptic to be used in the hospital. At t = 0 min, 100% of the bacteria are present on the test surface. Eighty minutes after the mixture of ethanol and acetone (i.e. antiseptic) is applied to the test surface, only 38% of the bacteria remain. Assuming that the percentage of bacteria remaining decays exponentially with time, determine when 15% of the original population of bacteria will remain.

Solution

We learned in an earlier section that this type of problem can be modeled by an exponential function of the form  (where a is the initial amount, b is the common ratio, and c is the time required for the common ratio to occur)

The initial amount is 100%, so a = 1.00; we have the data for when 38% of the mixture remains, so b = 0.38 ; this ratio occurs every eighty minutes, so c = 80. This particular bacteria population can thus be described by the equation:

where P is the population after time t.

Since the population that remains is 15% of the original, let P equal 0.15 in the equation and solve for t . This is shown in the step by step approach in the interactive below:

Activity

1. Read through the examples in Focus J on pages 178 - 180 in your text. 
2. Do the CYU Questions 9 - 14, 17 on pages 180 - 182.

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

Solve each of the following for x:

1.  
   
2. 

Solution