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Questions and Answers

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 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?

Reflection over the x-axis, horizontal translation 1 unit to the right, and vertical translation 5 units up Signup and view all the answers

Given the points (1, 28) and (2, 196), write an exponential equation in the form of f(x) = a(b)^x.

f(x) = 4(7)^x Signup and view all the answers

What is the value of 'a' in an exponential equation of the form f(x) = a(b)^x?

The y-intercept Signup and view all the answers

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.

A = 500(1 + 0.035/4)^(4t) Signup and view all the answers

What is the balance after 5 years in the account described in the previous question?

$595.17 Signup and view all the answers

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.

A = 2000(e^(0.023t)) Signup and view all the answers

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.

A = 38000(1 - 0.048)^t Signup and view all the answers

How much is the car worth after 4 years in the previous question?

$31212.70 Signup and view all the answers

What is the logarithmic form of the equation 7^3 = 49?

log₇(49) = 3 Signup and view all the answers

What is the exponential form of the equation log₃(81) = 4?

3^4 = 81 Signup and view all the answers

What is the domain of the logarithmic function graphed in the provided figure?

(0, ∞) Signup and view all the answers

What is the range of the logarithmic function graphed in the provided figure?

(-∞, ∞) Signup and view all the answers

What is the equation of the vertical asymptote of the logarithmic function graphed in the provided figure?

x=0 Signup and view all the answers

Solve for x: 2(4)^(2x+5)=25.

x ≈ 0.083 Signup and view all the answers

Solve for x: log₄(10)=2x.

x ≈ 0.830 Signup and view all the answers

Solve for x: 7^(x+1) + 8 = 73.

x ≈ 1.258 Signup and view all the answers

Solve for x: 2(5)^x + 8 = 120.

x ≈ 2.501 Signup and view all the answers

Solve for x: 9^(4x+1)=27^(3x-2).

x = 8 Signup and view all the answers

Solve for x: (x+2) + 10 = 12.

x = 0 Signup and view all the answers

Solve for x: 3(2x-3) = 9.

x = 3 Signup and view all the answers

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 = Pe^rt
- 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.