Functions  Exponential  main page.
The exponential function is important in explaining many events  especially those related to increasing or decreasing trends. It has the special characteristic that:
the rate at which the attribute being measured changes
is directly proportional to
the amount of that attribute at any given time.
Exponential equations are used in many situations  including finance (especially compound interest), growth of populations and radioactive decay.
The actual function was first considered in the context of a limiting value of a term by Jacob Bernoulli about 1683. In 1697, his brother Johann investigated the calculus of the exponential function. Leonhard Euler also joined the investigation at a later date (Johann had been his teacher).
The resources which can be accessed directly are:
1.The Amazing number e. 
2. Graphing exponential functions. 
3. Differentiation approaches to exponential functions. 
4. Integration of exponential functions. 
5. Application of exponential integration to equations. 
6. Area questions. 
7. Natural growth and decay  applications. 
8. Reverse Chain Rule questions. 
9. Differentiate ... hence find questions. 
10. Integration by substitution (nonRCR). 
Learning area  Resource 
Basic indices  Main page for indices for revision. 
The Amazing number e  Euler's number.  
Manipulating and graphing exponential functions.  
Manipulating and graphing exponential functions Test Yourself 1.  
Manipulating and graphing exponential functions  Test Yourself 1  Solutions. 

Differentiation of the exponential function.  
Exponential basic differentiation  Test Yourself 1. 

Exponential basic differentiation  Test Yourself 1  Solutions. 

Exponential basic differentiation  Test Yourself 2. 

Exponential basic differentiation  Test Yourself 2  Solutions. 

Applications of differerentiating exponentials.  Exponential differentiation applications (max/min, etc)  Test Yourself 1. 
Exponential differentiation applications (max/min, etc)  Test Yourself 1  Solutions.  
Multifunction differentiation with exponentials.  Multifunction differentiation  Test Yourself 1. 
Multifunction differentiation  Test Yourself 1  Solutions. 

Integration of the exponential function.  
Basic questions.  Exponential basic Integration  Test Yourself 1. 
Exponential basic Integration  Test Yourself 1  Solutions. 

Areas.  Exponential  integration  calculating areas  Test Yourself 1. 
Exponential  integration  calculating areas  Test Yourself 1  Solutions. 

Exponential  integration  calculating areas  Test Yourself 2. 

Exponential  integration  calculating areas  Test Yourself 2  Solutions. 

Natural growth and decay.  Natural Growth & decay  Test Yourself 1. 
Natural Growth & decay  Test Yourself 1  Solutions. 

Growth and decay  Test Yourself 2.  
Growth and decay  Test Yourself 2  Solutions.  
Modified natural growth and decay. (extension courses). 

Multifunction integration.  Multifunction integration  Test Yourself 1. 
Multifunction integration  Test Yourself 1  Solutions. 

Reverse Chain Rule.  Integration  RCR  Test Yourself 1. 
Integration  RCR  Test Yourself 1  Solutions.  
Differentiate ... hence find questions.  Differentiate  Hence find  Test Yourself 1. 
Differentiate Hence find  Test Yourself 1  Solutions. 
The basic strategies for differentiation are required for the exponential function also.
These strategies (including the Chain Rule, the Product Rule and the Quotient Rule) can be reviewed through the main differentiation page.