Exponential Functions Part 1
In this lesson on Exponential Functions Part 1, students will learn about the algebraic form of an exponential model and how to recognize its parameters, including the initial value and growth rate constant. They will also learn about the difference between absolute and relative rates and how to use them in exponential models. The lesson covers both discrete and continuous growth, and provides examples of how to calculate the growth factor and use it to evaluate exponential functions at different points. Students will also learn how to switch between the discrete and continuous forms of the exponential function.
Be familiar with and recognize the algebraic form for an exponential model, including the corresponding parameters and if those parameters have any meaning in the context of the functional relationship (e.g. does a parameter control the initial value, rate of change (shape), decreasing or increasing (flip), max/min, limiting values, etc.).
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- Problem Set - A problem set from this lesson.
- Problem Set Solutions - Solutions to the problem set form this lesson.
- Problem Set 2 With Solutions - A problem set with solutions included for this lesson.
- Notes - Notes from this lesson
- What is an exponential model?
- What are the parameters in an exponential model?
- What is the difference between a finite / discrete and a continuous exponential function?
- How do you find the initial value in an exponential model?
- What is the difference between a relative rate and an absolute rate?
- How do you calculate the relative rate of an exponential model at a particular time?
- What is growth factor for an exponential function and how do you find it?
- When does an exponential function increase / grow or decrease / decay?
- What happens to D(t) = ab^t when b > 1 or when 0 < b < 1?
- What happens to D(t) = ae^kt when k > 0 or when k < 0?
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Staff Review
This lesson explains the parameters of an exponential model and what they mean. Relative rate and growth rate of an exponential function is also explained. This is a great introduction to non-linear functions, and the problem sets are very helpful.
