ET_ Exponential Functions From Tables

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•
Mathematics, Other
•
9th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is an exponential function?
Back
An exponential function is a mathematical function of the form f(x) = a(b)^x, where 'a' is a constant, 'b' is the base of the exponential (a positive real number), and 'x' is the exponent.
2.
FLASHCARD QUESTION
Front
What does the base of an exponential function determine?
Back
The base of an exponential function determines the rate of growth or decay. If the base is greater than 1, the function represents exponential growth; if the base is between 0 and 1, it represents exponential decay.
3.
FLASHCARD QUESTION
Front
How can you identify an exponential function from a table of values?
Back
An exponential function can be identified from a table of values if the ratio of consecutive outputs (y-values) is constant when the inputs (x-values) are increased by the same amount.
4.
FLASHCARD QUESTION
Front
What is the general form of an exponential decay function?
Back
The general form of an exponential decay function is f(x) = a(b)^x, where 0 < b < 1.
5.
FLASHCARD QUESTION
Front
What is the general form of an exponential growth function?
Back
The general form of an exponential growth function is f(x) = a(b)^x, where b > 1.
6.
FLASHCARD QUESTION
Front
How do you write an exponential function from a given table of values?
Back
To write an exponential function from a table, identify the initial value (y-intercept) and the base by determining the constant ratio of the outputs for equal increments in the inputs.
7.
FLASHCARD QUESTION
Front
What is the significance of the initial value in an exponential function?
Back
The initial value in an exponential function represents the output when x = 0, which is the y-intercept of the graph.
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