What is the significance of the initial value in an exponential function?

The initial value $$a$$ in an exponential function $$y = ab^x$$ represents the value of $$y$$ when $$x = 0$$ , indicating the starting point of the function.

How do you convert a table of values into an exponential function?

To convert a table of values into an exponential function, identify the pattern of growth or decay, determine the base $$b$$ , and use the form $$y = ab^x$$ to find the constants.

What is the relationship between exponential functions and logarithms?

Exponential functions and logarithms are inverse functions. If $$y = b^x$$ , then $$x = \text{log}_b(y)$$ .

How do you solve for the base in an exponential equation?

To solve for the base in an exponential equation, isolate the exponential term and use logarithms to express the base in terms of the other variables.

What is the effect of changing the base in an exponential function?

Changing the base in an exponential function affects the rate of growth or decay. A larger base results in faster growth, while a smaller base (greater than 0) results in slower growth or faster decay.

How can you represent a real-world situation with an exponential function?

To represent a real-world situation with an exponential function, identify the initial quantity, the growth or decay rate, and express it in the form $$y = ab^x$$ .

What is the formula for exponential decay?

The formula for exponential decay is $$y = ae^{-kt}$$ , where $$a$$ is the initial amount, $$k$$ is the decay constant, and $$t$$ is time.

How do you graph an exponential function?

To graph an exponential function, plot the y-intercept, identify the base for growth or decay, and sketch the curve, ensuring it approaches the x-axis but never touches it.

Writing Exponential Functions Flashcard

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15 questions

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1.

FLASHCARD QUESTION

Front

What is an exponential function?

Back

2.

FLASHCARD QUESTION

Front

How do you identify the base in an exponential function?

Back

Tags

CCSS.HSF-IF.C.8B

3.

FLASHCARD QUESTION

Front

What does it mean for an exponential function to exhibit growth?

Back

Tags

CCSS.HSF-IF.C.8B

4.

FLASHCARD QUESTION

Front

What does it mean for an exponential function to exhibit decay?

Back

Tags

CCSS.HSF-IF.C.8B

5.

FLASHCARD QUESTION

Front

How can you write an exponential function from a graph?

Back

Tags

CCSS.HSF.LE.A.2

6.

FLASHCARD QUESTION

Front

What is the general form of an exponential function?

Back

7.

FLASHCARD QUESTION

Front

How do you determine the y-intercept of an exponential function?

Back

Tags

CCSS.HSF-IF.C.7E

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