Which of the following graphs shows an exponential graph and its inverse?

A.	B.
C.	D.

The restricted domain and range for an exponential function are given below.

Domain: {x│x ≥ 1}
Range: {y│y ≥ 3}

Which of the following describes the domain and range of its inverse?

1. Domain: {x│x ≥ 1}
   Range: {y│y ≥ 3}
2. Domain: {x│x ≥ -1}
   Range: {y│y ≥ -3}
3. Domain: {x│x ≥ 3}
   Range: {y│y ≥ 1}
4. Domain: {x│x ≤ 3}
   Range: {y│y ≤ 1}

What is the domain, range and vertical asymptote for f(x) = log₃(x − 5) + 2?

1. Domain: (5, ∞)
   Range: (- ∞, ∞)
   Vertical Asymptote: x = 5
2. Domain: (3, ∞)
   Range: (-∞, ∞)
   Vertical Asymptote: x = 3
3. Domain: (2, ∞)
   Range: (-∞, ∞)
   Vertical Asymptote: x = 2
4. Domain: (-5, ∞)
   Range: (-∞, ∞)
   Vertical Asymptote: x = -5

Below are some characteristics of an exponential function.

• Equation: y = 3^{x − h} + k
• Domain: (-∞, ∞)
• Horizontal asymptote: x = -2

Based on this information, what is the value of k?

1. Not enough information given.
2. k = 2
3. k = 0
4. k = -2

Christina plans to purchase a modular building for her new business priced at $60,000. Since this building will depreciate by 5% each year, she knows that the function for this situation can be modeled by V = 60,000∙(0.95)^t where V represents the value of the building over t years.

If the graph above represents this situations, solve the equation 40,000 = 60,000∙(0.95)^t.

1. t ≈ 22
2. t ≈ 14
3. t ≈ 4
4. t ≈ 8

Which of the following equations is the first step for solving the equation 9^{(x + 1)} = 27^2x using same bases?

1. 9^{(x + 1)} = 9^6x
2. 3^{(2x + 2)} = 3^6x
3. 3^{(x + 1)} = 3^2x
4. 27^{(3x + 3)} = 27^2x

Solve log₄(x − 6) + log₄(2x) = log₄x for x.

1. x = 6.5
2. x = 1.4
3. x = 7.8
4. No solution

What is the value of x in the equation log₈x = four-thirds 4 3 ?

1. x = 2
2. x = 16
3. x =
4. x = 6556 over 6561 6556 6561

What is the value of x in the equation log₈(x + 5) + log₃(2x) = log₃28?

1. x = 7.7
2. x = 3.4 or x = -3.4
3. x = -7 or x = 2
4. x = 2

Use a graphing method or table method to solve the inequality 25(2.1)^x > 50.

1. x ≤ .93
2. x ≥ .93
3. x > .93
4. x < .93

Recent research has placed Atascocita as the fastest growing city in Texas. According to Bloomberg Business, this city has shown a yearly increase of 8% since 2009.If Atascocita continues to grow at this rate, which exponential equation could be used to determine its population in 2012 assuming the population in 2009 was 40,947.(

1. 40,947 = p(1 + .08)³
2. P = 40,947(1 − .08)³
3. P = 40,947(1 + .08)³
4. P = 40,947(1 + 8)³

Iodine-123 is used to diagnose thyroid disease. Its half-life is about 13 hours as modeled by the formula A = A₀*0.5^t/13 where A₀ represents the initial amount and A represents amount after t hours. Suppose you begin with a sample of 15 grams, how long will it take to decay to 3 grams?

1. About 30.2 hours
2. About 12.8 hours
3. About 6.7 hours
4. About 5.2 hours

The table below shows the average daily number of vehicles that commute into the city of Metropolis for a 7 year period.

The city council decided that once the number of vehicles reaches 550,000, the city will begin to implement a commuter bus system. Find an exponential growth model that fits the data. Then use the model to approximate the year the city will implement a commuter bus system.

1. In the year 2013
2. In the year 2014
3. In the year 2015
4. In the year 2016

Below is a graph of an exponential function and its asymptote.

Which table represents values of its inverse?

The graph below shows the function f(x) = 4^x − 2, where x ≥ 0.

Which of the following correctly shows the range of the inverse of this function?

1. {y│y ≥ 0}
2. {y│y ≤ -1}
3. {y│y ≤ 0}
4. {y│y ≥ -1}

State the domain, range and horizontal asymptote for the exponential function f(x) = 2*5^{(x - 1)} + 3.

1. Domain: (-∞, ∞)
   Range: [2, ∞)
   Horizontal asymptote: x = 3
2. Domain: (-∞, ∞)
   Range: (3, ∞)
   Horizontal asymptote: y = 3
3. Domain: (-∞, ∞)
   Range: (3, ∞)
   Horizontal asymptote: y = 5
4. Domain: (3, ∞)
   Range: (-∞, ∞)
   Horizontal asymptote: y = 3

A log function in the form y = log_b(x + c) + d has been graphed below.

Based on this graph, which of the following best describes the domain, range and asymptote?

1. Domain: (-2, ∞)
   Range: [-∞, ∞)
   Asymptote: x = -2
2. Domain: (-∞, ∞)
   Range: [2, ∞)
   Asymptote: x = -2
3. Domain: (-2, ∞)
   Range: [-∞, ∞)
   Asymptote: y = -1
4. Domain: [-2, ∞)
   Range: (-∞, ∞)
   Asymptote: x = -2

The table below represents the equation y = 3 *

Based on this table, which of the following is a solution to the equation 3 = 3 *

1. {three-eighths 3 8 }
2. {0}
3. {24}
4. No solution

Which of the following could be the first step for solving the equation 5^{(x + 2)} = 3000?

1. log⁡5 + log⁡(x + 2) = log⁡3000
2. (x + 2)log3000 = log5
3. log5^{(x + 2)} = 3000
4. log5^{(x + 2)} = log3000

Robert plans to solve the equation log₃⁡(x² − 25) − log₃⁡(x − 5) = log₃ ⁡(2x − 1) using the table and/or graphing method on his calculator. Which of the following screen shot is a correct input to solve this equation?

A.	B.
C.	D.

The formula used to calculate the amount money, A, in an a savings account after t years is A = P(1 + r)^t, where P is the principal (or initial amount) and r is the interest rate. Mrs. Gonzalez is trying to determine how long it would take her savings account to double in value. If the interest rate is 4.5% and Mrs. Gonzalez does not make any additional deposits or withdraws, which of the following equations will determine how long it will take her money to double?

1. A = 2P(1 + 0.045)^t
2. A = P(1 + 0.045)^2t
3. 2P = P(1 + 0.045)^t
4. 2P = P(1 + 4.5)^2t

A biologist is observing a strain of bacteria that is growing exponentially in a Petri dish. If one bacteria took an hour to divide into 2 bacteria, which inequality will determine how long will it take for 20 bacteria in the disk to grow to at least 5000?

1. 20 * 2^x ≥ 5000
2. 2 * 20^x ≥ 5000
3. 20 * 2^x < 5000
4. 5000 ≥ 2^x

Use the graph below to solve the inequality 6(1.8)^x + 15 < 100?

1. (4.5, ∞)
2. [15, ∞)
3. [0, 4.5)
4. (15, 100)

According to statistics, the growth of the population age 65 and older has grown exponentially since the year 1900. The equation y = 3∙ 1.024^x represents the approximate growth of this population in millions, where x = 0 represents the year 1900; x = 1 represents the year 1901; and so on. Using this formula, predict the population in the year 2030.

1. 65.5 million
2. 158.9 million
3. 399.4 million
4. Not possible

What is the domain of the equation log₇(15 − 3x) − log₇(x − 2) = log₇x?

1. x > 2
2. x < 5
3. 5 < x < 7
4. 2 < x < 5