Math Problem Statement
Solution
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Question Breakdown:
1. Graph each exponential function.
-
f(x) = 3ᵡ:
This represents exponential growth with a base of 3. As x increases, y grows rapidly. -
f(x) = (1/4)ᵡ:
This represents exponential decay since the base (1/4) is less than 1. As x increases, y approaches 0. -
f(x) = 8·1.2ᵡ:
This is another growth function with an initial value of 8 (y-intercept when x = 0) and a growth factor of 1.2.
4-6. Write an equation for each exponential function.
- For each graph or table provided, analyze the growth/decay pattern to deduce the equation in the form , where is the initial value and is the base.
7. Key features of :
- Include details about the horizontal asymptote, key points (such as y-intercept and another point), domain (), and range ( for growth and for decay if ).
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Math Problem Analysis
Mathematical Concepts
Exponential Functions
Graphing Functions
Exponential Growth and Decay
Formulas
y = a·b^x (general exponential function)
Horizontal asymptote and domain/range relationships
Theorems
Properties of Exponential Functions
Key Points in Graphing Exponentials
Suitable Grade Level
Grades 8-10