What is the end behavior of the function $$f(x) = 3(2^x)$$ ?

As @@x ightarrow ext{-}\infty $$, $$ f(x) ightarrow 0 $$; as $$ x ightarrow ext{+}\\infty $$, $$ f(x) ightarrow ext{+}\\infty@@.

What is the range of the function $$f(x) = 5(3^x)$$ ?

The range of the function is all positive real numbers, represented as $$(0, \infty)$$ .

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

To find the y-intercept of an exponential function $$f(x) = a \times b^x$$ , evaluate $$f(0)$$ . The y-intercept is $$f(0) = a$$ .

What is the horizontal asymptote of the function $$f(x) = 2(3^x) - 4$$ ?

The horizontal asymptote is $$y = -4$$ .

What is the left end behavior of the function $$f(x) = 4(2^x)$$ ?

As @@x ightarrow -\infty $$, $$ f(x) ightarrow 0@@.

What is the right end behavior of the function $$f(x) = 5(4^x)$$ ?

As @@x ightarrow +\infty $$, $$ f(x) ightarrow +\infty@@.

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

Exponential functions do not have x-intercepts because they never cross the x-axis; they approach zero but never reach it.

What is the significance of the constant 'a' in the function $$f(x) = a \times b^x$$ ?

The constant 'a' represents the initial value or the y-intercept of the exponential function.

What is the formula for exponential growth?

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.

What is the formula for exponential decay?

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.

Exponential Characteristics Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is an exponential function?

Back

2.

FLASHCARD QUESTION

Front

What is the difference between exponential growth and exponential decay?

Back

3.

FLASHCARD QUESTION

Front

How do you express repeated multiplication using exponents?

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

What is the domain of an exponential function?

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

What does the base of an exponential function indicate?

Back

The base of an exponential function indicates the growth or decay factor. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

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