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Questions and Answers
What is the missing exponent in the expression $−4^{?}−2(4)$?
What is the missing exponent in the expression $−4^{?}−2(4)$?
What is the result of the expression $2^{-3} imes 4^{-2}$?
What is the result of the expression $2^{-3} imes 4^{-2}$?
Which of the following represents an exponential function based on the values for $x$ and $y$?
Which of the following represents an exponential function based on the values for $x$ and $y$?
If $y = 2^{x}$ for given inputs $x = 0, 1, 2, 3, 4$, what is the output for $x = 3$?
If $y = 2^{x}$ for given inputs $x = 0, 1, 2, 3, 4$, what is the output for $x = 3$?
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For the equation $y = 5x$, what is the value of $y$ when $x = 4$?
For the equation $y = 5x$, what is the value of $y$ when $x = 4$?
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Which of these equations correctly represents the exponential growth of bacteria, based on the values $0, 1, 2, 3, 4$ resulting in $1, 2, 6, 24, 120$?
Which of these equations correctly represents the exponential growth of bacteria, based on the values $0, 1, 2, 3, 4$ resulting in $1, 2, 6, 24, 120$?
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What is the value of $x$ in the expression $5x = 25$?
What is the value of $x$ in the expression $5x = 25$?
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What is the result of squaring the value represented by the expression $(3y) = b$ when $y = 2$?
What is the result of squaring the value represented by the expression $(3y) = b$ when $y = 2$?
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What type of function is represented by the values of $y$ from the set $x: [0, 1, 2, 3, 4, 5]$ and $y: [5/2, 5, 10, 20, 40, 80]$?
What type of function is represented by the values of $y$ from the set $x: [0, 1, 2, 3, 4, 5]$ and $y: [5/2, 5, 10, 20, 40, 80]$?
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What equation describes the relationship in the given data where $x: [1, 2, 3, 4, 5, 6]$ and $y: [6, 18, 54, 162, 486, 1458]$?
What equation describes the relationship in the given data where $x: [1, 2, 3, 4, 5, 6]$ and $y: [6, 18, 54, 162, 486, 1458]$?
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What type of growth does the function $y = 2(4)^x$ represent?
What type of growth does the function $y = 2(4)^x$ represent?
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For the equation $y = 875(1 - 0.13)^t$, what does the coefficient represent?
For the equation $y = 875(1 - 0.13)^t$, what does the coefficient represent?
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The population of Suzyville in 2025 can be represented by which of the following equations if it grows by 7% every year since 1997?
The population of Suzyville in 2025 can be represented by which of the following equations if it grows by 7% every year since 1997?
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What will be the value of the car on Suzy’s 21st birthday if it depreciates at 9% per year, starting from $20,000?
What will be the value of the car on Suzy’s 21st birthday if it depreciates at 9% per year, starting from $20,000?
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What will the number of bacteria be after 2 days if the bacteria grow at a rate of 3.5% per hour, starting with 350?
What will the number of bacteria be after 2 days if the bacteria grow at a rate of 3.5% per hour, starting with 350?
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Which of the following expressions represents the decay of the value of the equipment after $t$ years?
Which of the following expressions represents the decay of the value of the equipment after $t$ years?
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What is the simplified form of $5^{3} imes 5^{6}$?
What is the simplified form of $5^{3} imes 5^{6}$?
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Which expression correctly simplifies to $3x imes 5x$?
Which expression correctly simplifies to $3x imes 5x$?
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What is the simplified result of $(-2)^{5} imes 3^{3}$?
What is the simplified result of $(-2)^{5} imes 3^{3}$?
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What is the correct simplification of $(-3)^{-2} imes (2x)^{2}$?
What is the correct simplification of $(-3)^{-2} imes (2x)^{2}$?
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Which expression is equivalent to $x^{2}/(3xy)$?
Which expression is equivalent to $x^{2}/(3xy)$?
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What is the result of $3 imes (2x)^{2}$?
What is the result of $3 imes (2x)^{2}$?
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What does the expression $(2^{-5})^{2}$ simplify to?
What does the expression $(2^{-5})^{2}$ simplify to?
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Which expression correctly simplifies to $6^{-2} imes 3^{-3}$?
Which expression correctly simplifies to $6^{-2} imes 3^{-3}$?
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What is the simplified form of $3x(-2)^{3}$?
What is the simplified form of $3x(-2)^{3}$?
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Study Notes
Exponential Review
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Simplifying expressions: Various examples provided involve simplifying expressions with exponents. These include combining like terms, using exponent rules (product, quotient, power of a power), and handling negative exponents.
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Missing exponents: Problems involving finding the missing exponent in equations with variables and exponents. Examples include using the rules of exponents to solve equations for unknown exponents.
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Finding x and y: Find the values of x and y in equations involving exponents and variables based on given conditions. Functions and their relationships are key.
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Exponential function determination: Determine if given data represents a linear, exponential, or neither function.
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Graphing exponential functions: Graph exponential functions of the form y = a(b)x. The graphs involve understanding the basic exponential shape.
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Exponential growth/decay: Determine if the given functions of the form y = a(b)x represent exponential growth or decay.
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Functions for graphs: Create functions to describe provided graphs of exponential functions that pass specific points.
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Financial applications (depreciation, population): Problems involving exponential depreciation and growth (e.g., calculating future population or equipment value based on initial value and constant rate of change.)
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Bacterial growth: Applications of exponential growth to microbiology (representing bacterial growth given an initial quantity, rate of growth, and time.)
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Sequences (arithmetic/geometric): Problems to identify arithmetic and/or geometric sequences, deriving rules that represent them.
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Description
This quiz focuses on the principles of exponents and their applications in algebra. It includes simplifying expressions, solving for missing exponents, and graphing exponential functions. Additionally, you'll assess whether datasets represent linear or exponential functions and explore concepts of exponential growth and decay.
