What is an exponential function?
Writing Exponential Functions (Word Problems)

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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 the base (a positive real number), and 'x' is the exponent. It represents growth or decay processes.
2.
FLASHCARD QUESTION
Front
What does it mean for a function to model exponential growth?
Back
A function models exponential growth if the base 'b' is greater than 1, indicating that the quantity increases over time.
3.
FLASHCARD QUESTION
Front
What does it mean for a function to model exponential decay?
Back
A function models exponential decay if the base 'b' is between 0 and 1, indicating that the quantity decreases over time.
4.
FLASHCARD QUESTION
Front
How do you identify the initial value in an exponential function?
Back
The initial value in an exponential function f(x) = a(b)^x is represented by 'a', which is the value of the function when x = 0.
5.
FLASHCARD QUESTION
Front
What is the formula for exponential decay?
Back
The formula for exponential decay is f(t) = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.
6.
FLASHCARD QUESTION
Front
What is the formula for exponential growth?
Back
The formula for exponential growth is f(t) = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.
7.
FLASHCARD QUESTION
Front
How do you convert a percentage decay rate to a decimal for use in an exponential function?
Back
To convert a percentage decay rate to a decimal, divide the percentage by 100. For example, a 30% decay rate becomes 0.30.
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