AP Precalculus Section 2.5 Example: TI-84+ Calculator to Use 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!

The process to perform exponential regression on a TI-84 calculator and make predictions involves:

1. **Enter Data:** Input your x and y data pairs into lists, for example, x-values in L1 and y-values in L2.

2. **Perform Exponential Regression:**
- Press `STAT`.
- Choose "Edit" to input your data.
- Enter your x-values into one list and y-values into another.
- Press `STAT` again.
- Move to the "CALC" menu.
- Choose "ExpReg" (Exponential Regression).
- Select the lists containing your data.
- Press `ENTER`.

3. **View the Regression Equation:** The calculator will display the equation in the form \(y = ab^x\) or \(Y_1 = ae^{bx}\). Record the values of \(a\) and \(b\).

4. **Make a Prediction:** Substitute a known \(x\)-value into the equation and solve for \(y\). For instance, if you want to predict \(y\) for \(x = 10\):
- Use the regression equation: \(y = ab^x\) (or \(Y_1 = ae^{bx}\)).
- Plug in \(x = 10\) and use the constants \(a\) and \(b\) obtained.
- Calculate \(y\) using the formula.

5. **Graph the Regression Equation:** To visualize the regression line and your data points:
- Go to the graphing menu by pressing `Y=`.
- Enter the regression equation.
- Press `GRAPH` to plot the regression line along with your data points.

Remember, ensure that your predicted \(x\) values fall within the range of your original data for accurate predictions.

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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