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This document discusses properties and transformations of exponential functions, including stretch, compression, reflection, and horizontal and vertical translation. It also discusses the number e as the base for natural exponential functions and using the function A=Pe^rt to model continuously compounded interest. Examples are provided to demonstrate graphing transformations of exponential functions and using the continuously compounded interest formula.
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This module introduces exponential functions and their key properties. Students will learn to identify real-world relationships that are exponential, such as population growth. They will analyze tables of values to determine if a relationship is exponential. Students will also learn to graph common exponential functions like f(x)=ax and describe their properties, including domain, range, intercepts, trend, and asymptote. The lessons include examples of constructing tables, graphing functions, and analyzing exponential behavior.Math Subject: Exponential Functions .pptx
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The document covers exponential functions, including their definitions, properties, and examples of exponential growth and decay. It explains the equality property of exponential functions and details how to write exponential functions based on data points, as well as applications such as compound interest formulas. The document also includes examples and exercises related to these concepts.Bab 4 dan bab 5 algebra and trigonometry
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This document discusses exponential functions and their properties. Exponential functions have the form f(x) = ax, where a is the base. They model phenomena like population growth, compound interest, and radioactive decay. Exponential functions either increase or decrease rapidly depending on whether the base a is greater than or less than 1. Their graphs have a characteristic shape, with the x-axis as a horizontal asymptote. Logarithmic functions are the inverses of exponential functions and can be used to solve equations involving exponential models.Matematicas FINANCIERAS CIFF dob.pdf
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The document serves as a mathematics primer aimed at refreshing essential topics such as calculus, linear algebra, differential equations, and probability & statistics. It defines fundamental mathematical concepts and functions, emphasizing functions' roles in mapping domains to ranges, along with discussions on various types of functions and their properties. Additionally, the document covers limits, exponential and logarithmic functions, and trigonometric functions, illustrating mathematical behaviors and identities.Ad
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- 2. Transformations of Exponential Functions Note that the base of the parent is a variable, Parent: therefore there are infinite parents within the Exponential Family General Form: Stretch: Compression (shrink): Reflection: Horizontal Translation: Vertical Translation:
- 3. Graph each function as a transformation of its parent 1. Create a Table of Values for the parent 2. Plot the points and label the graph 3. If the transformation contains a stretch, compression, or reflection: Create a Table of Values for the transformed function (use the same x-values) and Plot the points and label the graph 4. If the transformation contains a simple horizontal or vertical translation: move the parent points appropriately
- 4. Examples
- 5. Examples
- 6. Examples
- 7. The Number e The Number e is an irrational number approximately equal to 2.71828 Exponential functions with base e are called natural base exponential functions. These exponential functions have the same properties as other exponential functions To graph functions with base e, use the e key on the calculator to get a decimal approximation
- 8. Continuously Compounded Interest To use this function: 1. Identify the value of the variables 2. Plug the known values into the equation 3. Solve for the unknown value
- 9. Example (p447) Suppose you won a contest at the start of 5th grade that deposited $3000 in an account that pays 5% annual interest compounded continuously. How much will you have in the account when you enter high school 4 years later? Express the answer to the nearest dollar.
- 10. Homework P447 #1 4 all, 7 27 odd, 28 31 all