What is the domain of the function $$y = 2^x$$ ?

The domain of the function $$y = 2^x$$ is all real numbers, expressed as @@(- ext{∞}, ext{∞})@@.

What is the range of the function $$y = 2^x$$ ?

The range of the function $$y = 2^x$$ is all positive real numbers, expressed as $$(0, \text{∞})$$ .

What is the result of $$2^3 \times 2^2$$ ?

The result is $$2^{3+2} = 2^5 = 32$$ .

What is the result of $$\frac{1}{2^3}$$ ?

The result is $$2^{-3} = \frac{1}{8}$$ .

What is the difference between exponential growth and exponential decay?

Exponential growth occurs when the base of the exponential function is greater than 1, leading to an increase over time. Exponential decay occurs when the base is between 0 and 1, leading to a decrease over time.

What is the equation for exponential decay?

The equation for exponential decay can be written as $$A = A_0 e^{-kt}$$ , where 'A_0' is the initial amount, 'k' is a positive constant, and 't' is time.

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

The graph of an exponential growth function rises steeply to the right and approaches the x-axis but never touches it.

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

The graph of an exponential decay function falls steeply to the right and approaches the x-axis but never touches it.

What is the value of $$2^0$$ ?

The value of $$2^0$$ is 1, as any non-zero number raised to the power of 0 equals 1.

What is the equation for the median household income that increased by 0.5% each month starting from $37,060?

The equation is $$A = 37060(1.005)^x$$ , where 'A' is the median income after 'x' months.

What is the property of exponents when dividing two exponential expressions with the same base?

When dividing two exponential expressions with the same base, you subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$ .

Exponential Functions and Equations Practice Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is an exponential function?

Back

2.

FLASHCARD QUESTION

Front

What does the base of an exponential function represent?

Back

The base of an exponential function determines the rate of growth or decay. If the base is greater than 1, the function represents exponential growth. If the base is between 0 and 1, it represents exponential decay.

Tags

CCSS.HSF-IF.C.8B

3.

FLASHCARD QUESTION

Front

Write the exponential equation for a quantity that increases by 5% each month starting from 100.

Back

Tags

CCSS.HSF.LE.A.2

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

According to the properties of exponents, what happens when you multiply two exponential expressions with the same base?

Back

Tags

CCSS.8.EE.A.1

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.8.EE.A.1

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