AP Precalculus Section 2.2 Example: TI-84+ Calculator to Find Exponential Regression (Predictions)

Random AP Precalculus Problems (I found on the Internet). These are not official AP Collegeboard examples, but they will definitely get the job done!

To find an exponential regression model on a TI-84+ calculator given two points, follow these steps:

1. **Enter Data:**
- Press the `STAT` button.
- Enter your x-values into a list in L1 and y-values into another list in L2.

2. **Set Up Exponential Regression:**
- Go back to the main screen by pressing `2nd` and then `MODE` to access the home screen.
- Press `STAT` again, then scroll right to the `CALC` menu.

3. **Choose Exponential Regression:**
- Scroll down or up to find and select `ExpReg` (exponential regression) from the list. Press `ENTER`.

4. **Select Lists:**
- The calculator will prompt you for the input lists. Enter the lists where your data is stored (e.g., L1 for x-values and L2 for y-values).
- Press `ENTER` after entering the lists.

5. **View Results:**
- The calculator will display the regression equation of the form \(y = ab^x\). The values of \(a\) and \(b\) are the coefficients of the regression model.

6. **Interpret the Equation:**
- The equation will help you predict \(y\) for a given \(x\) based on the exponential model you've obtained.

Remember that exponential regression might not be the best fit for all data sets. Verify the appropriateness of your model by examining the correlation coefficient (r) and considering the context of your data.

The Topics covered in AP Precalculus are...

1.1 Change in Tandem
1.2 Rates of Change
1.3 Rates of Change in Linear and Quadratic Functions
1.4 Polynomial Functions and Rates of Change
1.5 Polynomial Functions and Complex Zeros
1.6 Polynomial Functions and End Behavior
1.7 Rational Functions and End Behavior
1.8 Rational Functions and Zeros
1.9 Rational Functions and Vertical Asymptotes
1.10 Rational Functions and Holes
1.11 Equivalent Representations of Polynomial and Rational Expressions
1.12 Transformations of Functions
1.13 Function Model Selection and Assumption Articulation
1.14 Function Model Construction and Application
2.1 Change in Arithmetic and Geometric Sequences
2.2 Change in Linear and Exponential Functions
2.3 Exponential Functions
2.4 Exponential Function Manipulation
2.5 Exponential Function Context and Data Modeling
2.6 Competing Function Model Validation
2.7 Composition of Functions
2.8 Inverse Functions
2.9 Logarithmic Expressions
2.10 Inverses of Exponential Functions
2.11 Logarithmic Functions
2.12 Logarithmic Function Manipulation
2.13 Exponential and Logarithmic Equations and Inequalities
2.14 Logarithmic Function Context and Data Modeling
2.15 Semi-log Plots
3.1 Periodic Phenomena
3.2 Sine, Cosine, and Tangent
3.3 Sine and Cosine Function Values
3.4 Sine and Cosine Function Graphs
3.5 Sinusoidal Functions
3.6 Sinusoidal Function Transformations
3.7 Sinusoidal Function Context and Data Modeling
3.8 The Tangent Function
3.9 Inverse Trigonometric Functions
3.10 Trigonometric Equations and Inequalities
3.11 The Secant, Cosecant, and Cotangent Functions
3.12 Equivalent Representations of Trigonometric Functions
3.13 Trigonometry and Polar Coordinates
3.14 Polar Function Graphs
3.15 Rates of Change in Polar Functions

I have many informative videos for Pre-Algebra, Algebra 1, Algebra 2, Geometry, Pre-Calculus, and Calculus. Please check it out:

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Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa

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