What is the common ratio in exponential functions?

The common ratio in exponential functions is the base 'b' in the function $$y = a \times b^x$$ .

What is the difference between linear and exponential functions?

Linear functions have a constant rate of change, represented as $$y = mx + b$$ , while exponential functions have a variable rate of change, represented as $$y = a \times b^x$$ .

What does the variable 'a' represent in an exponential function?

In an exponential function $$y = a \times b^x$$ , 'a' represents the initial value or the y-intercept of the function.

What does the variable 'b' represent in an exponential function?

In an exponential function $$y = a \times b^x$$ , 'b' represents the base of the exponential function, which determines the growth or decay rate.

What happens to the graph of an exponential function as x approaches infinity?

As x approaches infinity, the graph of an exponential growth function increases without bound, while the graph of an exponential decay function approaches the horizontal asymptote (usually y=0).

What is the significance of the y-intercept in an exponential function?

The y-intercept of an exponential function, found at x=0, is equal to 'a' in the function $$y = a \times b^x$$ .

How can you determine if a function is exponential from a table of values?

A function is exponential if the ratio of consecutive outputs is constant, indicating a consistent multiplicative change.

What is the relationship between exponential functions and logarithms?

Exponential functions and logarithms are inverse functions; the logarithm of a number is the exponent to which the base must be raised to produce that number.

Exponential Functions Intro Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is an exponential function?

Back

2.

FLASHCARD QUESTION

Front

What characterizes exponential growth?

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to a rapid increase over time.

Tags

CCSS.HSF-IF.C.8B

3.

FLASHCARD QUESTION

Front

What characterizes exponential decay?

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value, leading to a rapid decrease over time.

Tags

CCSS.HSF-IF.C.8B

4.

FLASHCARD QUESTION

Front

What is the basic form of an exponential function?

Back

5.

FLASHCARD QUESTION

Front

What is the equation of the horizontal asymptote for exponential functions?

Back

Tags

CCSS.HSF-IF.C.7E

6.

FLASHCARD QUESTION

Front

How do you identify exponential growth from a function?

Back

Tags

CCSS.HSF-IF.C.8B

7.

FLASHCARD QUESTION

Front

How do you identify exponential decay from a function?

Back

Tags

CCSS.HSF-IF.C.8B

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