What is the definition of an exponential function?
24-25 T2U8 Test Review

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Mathematics
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9th - 12th 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.
2.
FLASHCARD QUESTION
Front
How do you determine the value of a function at a specific point, such as f(-3) for f(x) = 2(4)^x?
Back
To determine f(-3), substitute -3 for x in the function: f(-3) = 2(4)^(-3) = 2 * (1/64) = 1/32.
3.
FLASHCARD QUESTION
Front
What distinguishes a linear function from an exponential function?
Back
A linear function has a constant rate of change and can be represented by a straight line, while an exponential function has a variable rate of change that increases or decreases exponentially.
4.
FLASHCARD QUESTION
Front
What is the explicit formula for a geometric sequence?
Back
The explicit formula for a geometric sequence is f(n) = a * r^(n-1), where a is the first term, r is the common ratio, and n is the term number.
5.
FLASHCARD QUESTION
Front
How do you find the 10th term of a geometric sequence given the explicit formula f(n) = 3(4)^(n-1)?
Back
To find the 10th term, substitute n = 10 into the formula: f(10) = 3(4)^(10-1) = 3(4^9) = 786432.
6.
FLASHCARD QUESTION
Front
What is the relationship between the bases and exponents in exponential expressions?
Back
In exponential expressions, the base is raised to the power of the exponent, which indicates how many times the base is multiplied by itself.
7.
FLASHCARD QUESTION
Front
What does it mean for a function to be exponential in terms of growth?
Back
An exponential function exhibits rapid growth or decay, where the rate of change increases or decreases multiplicatively rather than additively.
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