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Questions and Answers
What is the horizontal asymptote of the function f(x)= -3^(x-1) + 5?
What is the horizontal asymptote of the function f(x)= -3^(x-1) + 5?
y=5
What is the domain of the function f(x)= -3^(x-1) + 5?
What is the domain of the function f(x)= -3^(x-1) + 5?
(-∞, ∞)
What is the range of the function f(x)= -3^(x-1) + 5?
What is the range of the function f(x)= -3^(x-1) + 5?
(-∞, 5)
What are the transformations applied to the parent function f(x)=3^x to obtain the function f(x)= -3^(x-1) + 5?
What are the transformations applied to the parent function f(x)=3^x to obtain the function f(x)= -3^(x-1) + 5?
Given the points (1, 28) and (2, 196), write an exponential equation in the form of f(x) = a(b)^x.
Given the points (1, 28) and (2, 196), write an exponential equation in the form of f(x) = a(b)^x.
What is the value of 'a' in an exponential equation of the form f(x) = a(b)^x?
What is the value of 'a' in an exponential equation of the form f(x) = a(b)^x?
You deposit $500 into an account that pays 3.5% annual interest compounded quarterly. Write an exponential function for the amount of money in your account.
You deposit $500 into an account that pays 3.5% annual interest compounded quarterly. Write an exponential function for the amount of money in your account.
What is the balance after 5 years in the account described in the previous question?
What is the balance after 5 years in the account described in the previous question?
You deposit $2000 into an account that pays 2.3% annual interest compounded continuously. Write an exponential function for the amount of money in your account.
You deposit $2000 into an account that pays 2.3% annual interest compounded continuously. Write an exponential function for the amount of money in your account.
You buy a brand-new car for $38,000. The value of the car depreciates by 4.8% each year. Write an exponential function that models the value of the car after t years.
You buy a brand-new car for $38,000. The value of the car depreciates by 4.8% each year. Write an exponential function that models the value of the car after t years.
How much is the car worth after 4 years in the previous question?
How much is the car worth after 4 years in the previous question?
What is the logarithmic form of the equation 7^3 = 49?
What is the logarithmic form of the equation 7^3 = 49?
What is the exponential form of the equation log₃(81) = 4?
What is the exponential form of the equation log₃(81) = 4?
What is the domain of the logarithmic function graphed in the provided figure?
What is the domain of the logarithmic function graphed in the provided figure?
What is the range of the logarithmic function graphed in the provided figure?
What is the range of the logarithmic function graphed in the provided figure?
What is the equation of the vertical asymptote of the logarithmic function graphed in the provided figure?
What is the equation of the vertical asymptote of the logarithmic function graphed in the provided figure?
Solve for x: 2(4)^(2x+5)=25.
Solve for x: 2(4)^(2x+5)=25.
Solve for x: logâ‚„(10)=2x.
Solve for x: logâ‚„(10)=2x.
Solve for x: 7^(x+1) + 8 = 73.
Solve for x: 7^(x+1) + 8 = 73.
Solve for x: 2(5)^x + 8 = 120.
Solve for x: 2(5)^x + 8 = 120.
Solve for x: 9^(4x+1)=27^(3x-2).
Solve for x: 9^(4x+1)=27^(3x-2).
Solve for x: (x+2) + 10 = 12.
Solve for x: (x+2) + 10 = 12.
Solve for x: 3(2x-3) = 9.
Solve for x: 3(2x-3) = 9.
Flashcards
Exponential Function
Exponential Function
A function of the form f(x) = a(b)^x, where 'a' is the initial value, 'b' is the base, and 'x' is the exponent.
Horizontal Asymptote
Horizontal Asymptote
A horizontal line that a graph approaches but never touches.
Compound Interest (n times)
Compound Interest (n times)
Interest calculated and added to the principal at regular intervals (e.g., quarterly, monthly).
Compound Interest (Continuously)
Compound Interest (Continuously)
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Growth Formula
Growth Formula
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Decay Formula
Decay Formula
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Logarithmic Form
Logarithmic Form
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Exponential Form
Exponential Form
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Logarithm
Logarithm
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Finding 'a' and 'b'
Finding 'a' and 'b'
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Domain
Domain
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Range
Range
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Solve for x
Solve for x
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Vertical Asymptote
Vertical Asymptote
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Exponential Equation
Exponential Equation
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y-intercept
y-intercept
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Transformation
Transformation
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Study Notes
Quiz 1
- Exponential Function Graphing: Graph exponential functions, plotting at least four points and including the horizontal asymptote.
- Horizontal Asymptote: A horizontal line that the graph approaches but never touches.
- Domain: All possible x-values for the function.
- Range: All possible y-values for the function.
- Y-intercept: The point where the graph crosses the y-axis (x = 0).
- Transformations: Reflection over the x-axis, vertical translations (up or down), vertical stretching/shrinking (dilation).
- Exponential Equation from Two Points: Finding the equation f(x) = a(b)x given two points (x1, y1) and (x2, y2).
- Solve for 'a' and 'b' using the given points.
Quiz 2
- Compound Interest (Formulas):
- Compounded Quarterly: A = P(1 + r/n)nt
- Compounded Continuously: A = Pert
- Where:
- A = Final amount
- P = Principal amount
- r = Interest rate
- n = Number of times interest is compounded per year
- t= Time in years
- e = Euler's number (approximately 2.718)
- Exponential Function Modeling: Use formulas to write an exponential function that models a given scenario (e.g., growth, decay).
- Finding Balance After a Time Period: Given an exponential function, calculate the balance (e.g., money in an account, value of an item) after a certain time period
Quiz 3
-
Logarithmic and Exponential Forms: Convert between logarithmic and exponential forms of equations.
-
Logarithmic Function Properties:
- Domain: Values of x for which the function is defined.
- Range: All possible output values for the function
- Increasing Interval
- Decreasing Interval
- Vertical Asymptote: A vertical line that the graph approaches but never touches.
-
Solving Exponential Equations: Use logarithms to solve exponential equations.
-
Solving Logarithmic Equations: Use logarithms to solve logarithmic equations.
General
- Rounding Instructions: Round answers for values to three decimal places.
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