What is the range of the function $$f(x) = a \times b^x$$ where $$b > 1$$ ?

The range is all real numbers greater than 0, expressed as $$y > 0$$ .

What is the domain of the function $$f(x) = a \times b^x$$ ?

The domain is all real numbers, expressed as $$x \in \mathbb{R}$$ .

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

As $$x$$ approaches infinity, the value of the exponential function approaches infinity if $$b > 1$$ .

What is the value of $$f(0)$$ in an exponential function $$f(x) = a \times b^x$$ ?

The value is $$f(0) = a$$ , since any number raised to the power of 0 is 1.

If a cliff loses elevation at a rate of 5% every millennium, how do you calculate its elevation after several millennia?

Use the formula $$E = E_0(1 - 0.05)^t$$ , where $$E_0$$ is the initial elevation, and $$t$$ is the number of millennia.

What is the effect of a negative exponent in an exponential function?

A negative exponent indicates a reciprocal, meaning $$b^{-n} = \frac{1}{b^n}$$ .

How do you express exponential growth as a function?

Exponential growth can be expressed as $$f(t) = f_0 e^{kt}$$ , where $$f_0$$ is the initial value, $$k$$ is the growth constant, and $$t$$ is time.

What is the significance of the base in an exponential function?

The base determines the rate of growth or decay; if $$b > 1$$ , the function represents growth, and if $$0

How do you determine the initial value in an exponential function?

The initial value is the value of the function when $$x = 0$$ , which is $$f(0) = a$$ .

What is the relationship between exponential functions and logarithms?

Exponential functions and logarithms are inverses of each other; if $$y = b^x$$ , then $$x = \log_b(y)$$ .

Math 1 - Exponential Functions Test Review 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

How do you calculate the amount of growth in an exponential function?

Back

Tags

CCSS.HSF-IF.C.8B

3.

FLASHCARD QUESTION

Front

What is the formula for exponential decay?

Back

Tags

CCSS.HSF-IF.C.8B

4.

FLASHCARD QUESTION

Front

If a population doubles every month, what is the growth factor?

Back

The growth factor is 2, meaning the population multiplies by 2 each month.

Tags

CCSS.HSF-LE.A.1A

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

How do you find the number of months it takes for an amount to decrease to a certain value in exponential decay?

Back

Tags

CCSS.HSF.LE.A.4

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