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Definition
An exponential function is a mathematical function of the form:
where:
- a is a nonzero constant (the initial value or coefficient),
- b is the base of the exponential (a positive real number not equal to 1),
- x is the exponent (the independent variable).
The defining characteristic of an exponential function is that the variable xxx appears in the exponent.
Summary
Properties: Such as the rate of change, growth/decay behavior, and asymptotes.
Graphing: Exponential functions have graphs that pass through (0,a)(0, a)(0,a), increase rapidly for growth, and decrease towards zero for decay.
Real-World Applications:
- Population growth
- Radioactive decay
- Compound interest
- Spread of diseases or information
Comparisons with Other Functions: Unlike linear functions, the rate of change in exponential functions is proportional to their current value
Exponential Functions Math Activities
This is a fantastic bundle which includes 10 activities with answer guides about Exponential Functions. All our worksheets are completely editable so can be tailored for your curriculum and target audience.
Resource Examples
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Worksheets Activities Included
- Evaluate and Compare
- Growth or Decay?
- Fill in the Table
- Graph & Observe
- Solve for x
- Half-Life Challenge
- Doubling Time Puzzle
- Exponential vs Linear
- Transformations
- Real-Life Application