Podcast
Questions and Answers
What is the horizontal asymptote of the function f(x) = -3(3)^(x-1) + 5?
What is the horizontal asymptote of the function f(x) = -3(3)^(x-1) + 5?
y = 5
What is the domain of the function f(x) = -3(3)^(x-1) + 5?
What is the domain of the function f(x) = -3(3)^(x-1) + 5?
(-∞, ∞)
What is the range of the function f(x) = -3(3)^(x-1) + 5?
What is the range of the function f(x) = -3(3)^(x-1) + 5?
(-∞, 5)
What transformations are applied to the function f(x) = 3^(x) to get the function f(x) = -3(3)^(x-1) + 5?
What transformations are applied to the function f(x) = 3^(x) to get the function f(x) = -3(3)^(x-1) + 5?
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What is the formula for compound interest?
What is the formula for compound interest?
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What is the formula for continuously compounded interest?
What is the formula for continuously compounded interest?
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Write the exponential function that describes the amount of money in an account that pays 3.5% annual interest compounded quarterly if $500 is deposited initially.
Write the exponential function that describes the amount of money in an account that pays 3.5% annual interest compounded quarterly if $500 is deposited initially.
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What is the balance in the account after 5 years?
What is the balance in the account after 5 years?
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Write the exponential function that describes the amount of money in an account that pays 2.3% annual interest compounded continuously if $2000 is deposited initially.
Write the exponential function that describes the amount of money in an account that pays 2.3% annual interest compounded continuously if $2000 is deposited initially.
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Write the exponential function that models the value of a car that depreciates by 4.8% each year if the initial value is $38,000.
Write the exponential function that models the value of a car that depreciates by 4.8% each year if the initial value is $38,000.
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How much is the car worth after 4 years?
How much is the car worth after 4 years?
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The logarithmic form of the equation 7^3 = 49 is log_7 ______ = 3
The logarithmic form of the equation 7^3 = 49 is log_7 ______ = 3
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The exponential form of the equation log_3 2 = 1/2 is 3^______ = 2.
The exponential form of the equation log_3 2 = 1/2 is 3^______ = 2.
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The logarithmic form of the equation 10^-3 = 0.001 is log_10 ______ = -3
The logarithmic form of the equation 10^-3 = 0.001 is log_10 ______ = -3
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What is the domain of the logarithmic function graphed in the image?
What is the domain of the logarithmic function graphed in the image?
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What is the range of the logarithmic function graphed in the image?
What is the range of the logarithmic function graphed in the image?
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What is the vertical asymptote of the logarithmic function graphed in the image?
What is the vertical asymptote of the logarithmic function graphed in the image?
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Solve the equation 2(4)^(2x) + 5 = 25 for x (round to three decimal places).
Solve the equation 2(4)^(2x) + 5 = 25 for x (round to three decimal places).
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Solve the equation log_4(10) = 2x for x (round to three decimal places).
Solve the equation log_4(10) = 2x for x (round to three decimal places).
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Solve the equation 7^(x+1) + 8 = 73 for x (round to three decimal places).
Solve the equation 7^(x+1) + 8 = 73 for x (round to three decimal places).
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Solve the equation 2(5)^x + 8 = 120 for x (round to three decimal places)
Solve the equation 2(5)^x + 8 = 120 for x (round to three decimal places)
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Solve the equation 9^(4x+1) = 27^(3x-2) for x.
Solve the equation 9^(4x+1) = 27^(3x-2) for x.
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Solve the equation 8^(x+2) = (1/8)^5 for x.
Solve the equation 8^(x+2) = (1/8)^5 for x.
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Solve the equation 2^(x+2) = 4^(x+4) for x.
Solve the equation 2^(x+2) = 4^(x+4) for x.
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Solve the equation (x + 2) + 10 = 12 for x.
Solve the equation (x + 2) + 10 = 12 for x.
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Solve the equation 3(2x - 3) = 9 for x.
Solve the equation 3(2x - 3) = 9 for x.
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Study Notes
Quiz 1
- Graphing Exponential Functions: Plot at least four points and include the horizontal asymptote in the sketch.
- Horizontal Asymptote: A horizontal line the graph approaches but never touches.
- Domain: All real numbers (-∞, ∞) is common for exponential functions.
- Range: The range is limited from the horizontal asymptote.
- y-intercept: The point where the graph intersects the y-axis.
- Transformations: Reflection over the x-axis, vertical shifts, and horizontal stretches/compressions.
Exponential Equations
-
Form:
f(x) = a(b)^xwhere 'a' is the y-intercept and 'b' is the base. - Two Points to Find Equation: Use two given points to find 'a' and 'b', then write the equation.
Quiz 2: Compound Interest
-
Compound Interest Formula (n times per year):
A = P(1 + r/n)^(nt)where 'A' is the final amount, 'P' is the principal, 'r' is the annual interest rate, 'n' is the number of times interest is compounded per year, and 't' is the time in years. -
Compound Interest Formula (continuously):
A = Pe^(rt)where 'e' is Euler's number (approximately 2.718).
Quiz 2: Depreciation
-
Exponential Decay Formula:
A = P(1 - r)^t, where 'A' is the final amount, 'P' is the initial amount, 'r' is the decay rate, and 't' is the time.
Quiz 3: Logarithmic Equations
- Logarithmic Form: Equivalent to exponential form. Eg. logₐb = c represents a^c = b.
- Exponential Form: Convert logarithmic equations into exponential form and vice versa.
- Properties of Logarithmic Functions (from graph): include Domain, Range, Increasing/Decreasing Intervals, and Vertical Asymptote.
- Solving Equations Logarithms: Use logarithm properties to isolate the variable and solve for x. Round answers to three decimal places.
Solving Equations (General)
- Algebraic Methods: Use algebraic methods to solve equations for 'x'.
- Checking Solutions: Always check solutions in the original equation.
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Description
This quiz covers key concepts related to graphing exponential functions, including finding the horizontal asymptote, domain, range, and transformations. It also examines the compound interest formula and its components for calculating the final amount.
