Nov. 2 Class

Today we began by working on horizontal stretches of exponential functions, but then a majority of the class complained it was too easy!  So we moved on to discusse word problems and applications of exponential growth and decay.

Handouts:

• Investigating Transformations
• Transforming Exponential Functions

Here are some examples of horizontal stretches and compressions:

And just for fun, here are all the possible reflections:

Remember that bases can change too!

You all complained for more difficult examples, so here is one.  Try to sketch the following.

The first step is to use the exponent rules to rewrite the expression in a more recognizable form.  Then you can write out the transformations and you should get this graph:

Exponential Growth and Decay

Things that grow and decay can be modelled by exponential functions.  I told a story of a man who goes to ask the Emperor for rice.  He asked for one grain of rice on the first square of a chess board and asked to double it on each adjacent square until the board was full.  What function would model the amount of rice in each square?  The answer is an exponential function of base 2.

Here are the notes I gave in class:

This example was meant to show you how the general formula was derived.  Once you know the general formula, you should it from now on. 

This will model all the examples of exponential growth or decay.  In the case of exponential decay, the formula would contain a negative 'r' value and it would be called the "decay rate".

Homework: 

• Complete all graphing worksheets.  
• P. 251 # 1-11 
• P. 261-263 # 5-11