What is an exponential function?
Exponential Functions

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Mathematics
•
9th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Back
An exponential function is a mathematical function of the form f(x) = a(b^x), where 'a' is a constant, 'b' is a positive real number, and 'x' is the exponent. It shows rapid growth or decay.
2.
FLASHCARD QUESTION
Front
What is the difference between exponential growth and exponential decay?
Back
Exponential growth occurs when a quantity increases by a constant percentage over time, while exponential decay occurs when a quantity decreases by a constant percentage over time.
3.
FLASHCARD QUESTION
Front
What is the general form of an exponential growth function?
Back
The general form is f(x) = a(1 + r)^x, where 'a' is the initial amount and 'r' is the growth rate.
4.
FLASHCARD QUESTION
Front
What is the general form of an exponential decay function?
Back
The general form is f(x) = a(1 - r)^x, where 'a' is the initial amount and 'r' is the decay rate.
5.
FLASHCARD QUESTION
Front
How do you identify an exponential growth graph?
Back
An exponential growth graph rises steeply as x increases, showing a J-shaped curve.
6.
FLASHCARD QUESTION
Front
How do you identify an exponential decay graph?
Back
An exponential decay graph falls steeply as x increases, approaching the x-axis but never touching it.
7.
FLASHCARD QUESTION
Front
What is the y-intercept of an exponential function?
Back
The y-intercept is the initial value of the function, found by evaluating f(0). For f(x) = a(b^x), it is 'a'.
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