Identify the base in the exponential function $$f(x) = 10(1.01)^x$$ .

The base of the function is $$1.01$$ .

What is the y-intercept of the function $$f(x) = 5 \times 2^x$$ ?

The y-intercept is the value of $$f(0)$$ , which is $$5 \times 2^0 = 5$$ .

What is the general form of an exponential decay function?

The general form is $$f(x) = a \times (1 - r)^x$$ , where $$0

What is the value of $$f(3)$$ for the function $$f(x) = 10(1.01)^x$$ ?

$$f(3) = 10(1.01)^3 \\ = 10 \times 1.030301 = 10.30301$$ .

How can you identify the y-intercept from an exponential function?

The y-intercept can be found by evaluating the function at $$x = 0$$ .

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

Changing the base affects the rate of growth or decay; a larger base results in faster growth, while a base between 0 and 1 results in decay.

What is the domain and range of an exponential function?

The domain of an exponential function is all real numbers (i.e., @@(- ext{∞}, ext{∞}) $$), and the range is positive real numbers (i.e., $$ (0, ext{∞})@@).

What is the horizontal asymptote of an exponential decay function?

The horizontal asymptote of an exponential decay function is the x-axis, or $$y = 0$$ .

How do you classify the function $$A = 10(1.01)^3$$ ?

This function represents exponential growth because the base $$1.01 > 1$$ .

What is the equation of the exponential function that passes through the point (0, 3)?

The equation can be written as $$f(x) = 3 \times b^x$$ , where $$b$$ is the base.

Exponential Functions 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

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

How do you determine if a function is exponential?

Back

6.

FLASHCARD QUESTION

Front

What does the graph of an exponential growth function look like?

Back

7.

FLASHCARD QUESTION

Front

What does the graph of an exponential decay function look like?

Back

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