Exponential and Logarithmic Functions Quiz: Test Your Understanding

Question 1

Which graph represents the exponential function f(x) = 3^x?

Accepted Answer

A curve that increases at an increasing rate

Answer

A straight line with a constant slope

Answer

A curve that decreases at a decreasing rate

Answer

A horizontal line parallel to the x-axis

Question 2

Solve the exponential equation: 3^(x-1) = 27

Accepted Answer

x = 4

Answer

x = 2

Answer

x = 3

Answer

x = 5

Question 3

Identify the inverse function of y = 2^x

Accepted Answer

y = log_2(x)

Answer

y = e^x

Answer

y = 10^x

Answer

y = x^2

Question 4

Determine the equation of the exponential function that best fits the data points {(1, 2), (2, 4), (3, 8), (4, 16)}

Accepted Answer

y = 2^x

Answer

y = x^2

Answer

y = e^x

Answer

y = log_2(x)

Question 5

A colony of bacteria grows exponentially. The initial population is 1000, and the population doubles every 3 hours. Calculate the population after 12 hours.

Accepted Answer

32000

Answer

4000

Answer

8000

Answer

16000

Question 6

Which of the following graphs represents the exponential function f(x) = 2^x?

Accepted Answer

An exponential curve increasing from left to right

Answer

A parabola opening upward

Answer

A parabola opening downward

Answer

An exponential curve decreasing from left to right

Question 7

Which of the following is the logarithmic form of the exponential equation 5^2 = 25?

Accepted Answer

log5(25) = 2

Answer

2log5(5) = 25

Answer

log25(5) = 2

Answer

2log25(5) = 5

Question 8

Which of the following functions represents exponential growth?

Accepted Answer

f(x) = 2^x

Answer

f(x) = 2x

Answer

f(x) = log2(x)

Answer

f(x) = x^2

Question 9

A population of bacteria doubles every hour. If there are initially 100 bacteria, write an exponential function that models the population growth.

Accepted Answer

f(x) = 100(2)^x

Answer

f(x) = 100(2)^(-x)

Answer

f(x) = 200(2)^x

Answer

f(x) = 200(2)^(-x)

Question 10

Which of the following is the inverse function of f(x) = log2(x)?

Accepted Answer

f^-1(x) = 2^x

Answer

f^-1(x) = log2(x^2)

Answer

f^-1(x) = x^2

Answer

f^-1(x) does not exist

Question 11

Which of the following is the domain of the function f(x) = log(x-2)?

Accepted Answer

x > 2

Answer

x >= 2

Answer

x < 2

Answer

x <= 2

Question 12

A town's population is currently 5,000 and is growing at a rate of 5% per year. Write an exponential equation that models this growth.

Accepted Answer

P = 5,000(1.05)^t

Answer

P = 5,000e^(0.05t)

Answer

P = 5,000 + 0.05t

Question 13

Which of the following is the graph of the exponential function f(x) = 2^x?

Accepted Answer

An exponential curve that increases rapidly

Answer

A straight line with a positive slope

Answer

An upward-opening parabola

Answer

A logarithmic curve that decreases slowly

Question 14

Which of the following is the inverse function of f(x) = log(x)?

Accepted Answer

f^-1(x) = e^x

Answer

f^-1(x) = 10^x

Answer

f^-1(x) = 2^x

Answer

f^-1(x) = x^e

Question 15

What is the domain of the exponential function f(x) = e^(x-1)?

Accepted Answer

All real numbers

Answer

x > 1

Answer

x < 1

Answer

x = 1

Question 16

Which of the following is the equation of the horizontal asymptote of the function f(x) = (2^x) / (2^x + 1)?

Accepted Answer

y = 1

Answer

y = 0

Answer

y = 2

Answer

y = -1

Question 17

Which of the following is the graph of the exponential function f(x) = 2^x?

Accepted Answer

An exponential curve that increases rapidly

Answer

A straight line with a positive slope

Answer

A parabola opening upwards

Answer

A logarithmic curve that decreases rapidly

Question 18

Which of the following represents the equation of a horizontal asymptote for the exponential function f(x) = e^(-x)?

Accepted Answer

y = 0

Answer

y = e

Answer

y = 1

Answer

No horizontal asymptote

Question 19

What is the domain of the function f(x) = log(x - 2)?

Accepted Answer

x > 2

Answer

x ≥ 2

Answer

x < 2

Answer

x ≤ 2

Question 20

Which of the following is the inverse function of f(x) = 2^x?

Accepted Answer

f^(-1)(x) = log2(x)

Answer

f^(-1)(x) = x

Answer

f^(-1)(x) = x^2

Answer

f^(-1)(x) is undefined

Question 21

Solve for x: e^(2x - 1) = 5

Accepted Answer

x = 1 + ln5/2

Answer

x = 2 + ln5/2

Answer

x = 1 - ln5/2

Answer

x = 2 - ln5/2

Question 22

Determine the equation of the exponential function having a base of 2 and a y-intercept of 3. Express your answer in the form y = a * b^x + c, where a, b, and c are constants.

Accepted Answer

y = 3 * 2^x + 3

Answer

y = 3 * 2^x - 3

Answer

y = 2 * 3^x + 3

Answer

y = 2 * 3^x - 3

Question 23

A bacteria culture doubles every hour. If there are initially 100 bacteria, how many bacteria will be present after 5 hours?

Accepted Answer

1600

Answer

200

Answer

400

Answer

800

Question 24

Rewrite the equation y = 10^(2x - 1) in logarithmic form.

Accepted Answer

log base 10 y = 2x - 1

Answer

log base y 10 = 2x - 1

Answer

2x - 1 = log base 10 y

Answer

2x - 1 = log base y 10

Question 25

Determine the domain of the function f(x) = ln(x - 2).

Accepted Answer

x > 2

Answer

x ≥ 2

Answer

x < 2

Answer

x ≤ 2

Question 26

A radioactive substance has a half-life of 12 hours. If there are initially 500 grams of the substance, how much will remain after 24 hours?

Accepted Answer

250 grams

Answer

125 grams

Answer

375 grams

Answer

500 grams

Question 27

Find the inverse function for the logarithmic equation: f(x) = log base 10 (4x + 5).

Accepted Answer

f^-1(x) = (10^x - 5)/4

Answer

f^-1(x) = (4x + 5)^-1

Answer

f^-1(x) = e^(4x + 5)

Answer

f^-1(x) = 1/(4x + 5)

Question 28

Which of the following best describes the graph of the function f(x) = 2^x?

Accepted Answer

An exponential curve that increases rapidly

Answer

A straight line with a positive slope

Answer

A straight line with a negative slope

Answer

An exponential curve that decreases rapidly

Question 29

What is the equation of the exponential function that passes through the points (0, 3) and (2, 12)?

Accepted Answer

f(x) = 3(2^x)

Answer

f(x) = 2(3^x)

Answer

f(x) = 4(2^x)

Answer

f(x) = 3(4^x)

Question 30

Which of the following is the inverse function of f(x) = log₂(x)?

Accepted Answer

f(x) = 2^x

Answer

f(x) = log₁₀(x)

Answer

f(x) = e^x

Answer

f(x) = ln(x)

Question 31

What is the domain of the function f(x) = ln(x-2)?

Accepted Answer

x > 2

Answer

x < 2

Answer

x ≥ 2

Answer

x ≤ 2

Question 32

Which of the following logarithmic equations is equivalent to the exponential equation 2^x = 8?

Accepted Answer

log₂(8) = x

Answer

log₈(2) = x

Answer

log₂(x) = 8

Answer

log₈(x) = 2

Question 33

An exponential function models a population that doubles every 5 hours. Which equation represents this function?

Accepted Answer

y = 2^(x/5)

Answer

y = 2^5x

Answer

y = 5^2x

Answer

y = 5^(x/2)

Question 34

Determine the domain and range of the logarithmic function f(x) = log2(x).

Accepted Answer

Domain: x > 0; Range: R

Answer

Domain: x < 0; Range: R

Answer

Domain: x > 0; Range: y > 0

Answer

Domain: x < 0; Range: y < 0

Question 35

Convert the logarithmic equation log10(5) = 0.6990 to its equivalent exponential form.

Accepted Answer

5 = 10^0.6990

Answer

10 = 5^0.6990

Answer

0.6990 = 10^5

Answer

0.6990 = 5^10

Question 36

Determine the inverse of the exponential function h(x) = 2^x.

Accepted Answer

h^-1(x) = log2(x)

Answer

h^-1(x) = 2^(-x)

Answer

h^-1(x) = logx(2)

Answer

h^-1(x) = 2^(logx)

Question 37

What is the equation of the exponential function with a base of 2 and a y-intercept of 4?

Accepted Answer

y = 4(2)^x

Answer

y = 2x^4

Answer

y = 2(4)^x

Answer

y = 4x^2

Question 38

Evaluate log₅(125)

Accepted Answer

3

Answer

2

Answer

5

Answer

4

Question 39

Simplify the expression: 3log₂(x) + 2log₂(y)

Accepted Answer

log₂(x³y²)

Answer

log₂(xy²)

Answer

log₂(x²y³)

Answer

log₂(x³ + y²)

Question 40

The population of a city grows exponentially at a rate of 2% per year. If the current population is 50,000, what will the population be in 10 years?

Accepted Answer

60,490 people (approximately)

Answer

70,000 people

Answer

55,000 people

Answer

65,000 people

Question 41

What is the inverse of the exponential function y = 2^x?

Accepted Answer

x = log₂(y)

Answer

x = 2y

Answer

y = 2x

Answer

x = y²

Question 42

Solve the following system of equations: 2^x + y = 5 and log₂(x + y) = 1

Accepted Answer

x = 2, y = 1

Answer

x = 3, y = 2

Answer

x = 1, y = 2

Answer

x = 2, y = 3