- Perform exponential regression
- Convert between exponential and continuous growth
- Compare exponential and linear regressions for best fit
The Main Idea
Exponential growth occurs when a quantity grows in proportion to itself, such as in population growth or compound interest. This type of growth is characterized by rapid expansion over time.
Key Concepts:
- Exponential Regression: Fitting an exponential function to a set of data using software tools.
- Continuous Growth: A form of exponential growth where the base of the exponential function is the irrational number [latex]e[/latex] commonly found in natural growth processes.
Comparing Exponential and Continuous Growth Formulas:
- Exponential Growth Formula: [latex]P_{n}=P_{0}(1+r)^{n}[/latex]
- Continuous Growth Formula: [latex]y = ae^{rx}[/latex]
- These formulas are used to model different types of growth scenarios, each with its unique characteristics.
Understanding how to convert between exponential and continuous growth models allows for flexibility in modeling various real-world scenarios.
Steps for Conversion:
- Identify the Formulas: Recognize the exponential growth formula [latex]P_{n}=P_{0}(1+r)^{n}[/latex] and the continuous growth formula [latex]y = ae^{rx}[/latex].
- Use Properties of Exponents: Apply the power rule of exponents to convert between the two forms.
- Equating Bases: By equating the bases in the formulas, you can transform one model into the other.
Watch the following video for a demonstration of how to use a graphing calculator to obtain a regression formula and use it to make a prediction.
You can view the transcript for “Ex: Perform Exponential Regression on a Graphing Calculator” here (opens in new window).