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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

In this video, I thoroughly describe and reteach the main components of the sections listed above found in the official College Board AP Precalculus course description found at [ Ссылка ]. Afterwords, I provide multiple examples and give descriptive solutions to AP Precalculus-style problems. Topics in this video include…

1. **Arithmetic Sequences:** Arithmetic sequences are lists of numbers with a common difference between each consecutive term. The explicit formula for the "n-th" term of an arithmetic sequence is given by: a_n = a_1 + (n - 1)d, where "a_1" is the first term, "d" is the common difference, and "n" is the term position.

2. **Geometric Sequences:** Geometric sequences are sequences where each term is found by multiplying the previous term by a constant called the common ratio. The explicit formula for the "n-th" term of a geometric sequence is: a_n = a_1 * r^(n-1), where "a_1" is the first term, "r" is the common ratio, and "n" is the term position.

3. **Equations of Exponential Functions:** Exponential functions are represented by the equation f(x) = a * b^x, where "a" and "b" are constants. "a" is the initial value, and "b" is the base, which determines the growth or decay rate.

4. **Transformations of Exponential Functions:** Transformations involve modifying the behavior of exponential functions. Common transformations include shifting the graph vertically or horizontally, stretching or compressing it, and reflecting it across the x-axis.

5. **Exponential Regression on the TI-84+ Calculator:** Exponential regression on a TI-84+ calculator is a statistical technique used to find an exponential model that best fits a set of data points. It helps determine the values of "a" and "b" in the exponential function f(x) = a * b^x.

6. **Exponential Function Manipulation:** This involves solving and rewriting exponential functions with the same base to simplify equations. Common techniques include changing all bases to the same base or combining exponential terms to simplify expressions.

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

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