Exponential Functions

Question 1

What is the general form of an exponential function?

Answer 1

f(x) = a * b^x, where a is a constant, b is the base, and x is the exponent.

Question 2

True or False: The base of an exponential function must always be greater than 1.

Answer 2

False. The base can be any positive number, including a fraction between 0 and 1.

Question 3

What is the value of b in the exponential function f(x) = 3 * 2^x?

Answer 3

2

Question 4

Fill in the blank: An exponential function with a base greater than 1 is known as __________.

Answer 4

exponential growth

Question 5

Fill in the blank: An exponential function with a base between 0 and 1 is known as __________.

Answer 5

exponential decay

Question 6

What is the y-intercept of the function f(x) = 5 * 3^x?

Answer 6

5

Question 7

Which of the following represents exponential growth? a) f(x) = 2^x, b) f(x) = (1/2)^x

Answer 7

a) f(x) = 2^x

Question 8

What is the domain of the function f(x) = 4 * (1/2)^x?

Answer 8

All real numbers

Question 9

True or False: The graph of an exponential function can never touch the x-axis.

Answer 9

True

Question 10

What is the horizontal asymptote of the function f(x) = 2^x?

Answer 10

y = 0

Question 11

If f(x) = 7 * (0.8)^x, what type of function is this?

Answer 11

Exponential decay

Question 12

What happens to the value of f(x) as x approaches infinity for f(x) = 3 * 2^x?

Answer 12

f(x) approaches infinity.

Question 13

In the function f(x) = 10 * 5^x, what is the growth factor?

Answer 13

5

Question 14

Calculate f(2) for the function f(x) = 2^x.

Answer 14

4

Question 15

What is the range of any exponential function?

Answer 15

All positive real numbers.

Question 16

True or False: The graph of an exponential function can be symmetric.

Answer 16

False

Question 17

What is the formula for continuous exponential growth?

Answer 17

A(t) = A_0 * e^(rt), where A_0 is the initial amount, r is the rate, and t is time.

Question 18

If an exponential function has a base of e, what type of function is it?

Answer 18

Natural exponential function

Question 19

What is the value of f(0) for f(x) = 4 * (3)^x?

Answer 19

4

Question 20

Which of the following functions represents exponential decay? a) f(x) = 2^x, b) f(x) = (1/3)^x

Answer 20

b) f(x) = (1/3)^x

Question 21

What is the effect of increasing the base in an exponential growth function?

Answer 21

It increases the rate of growth.

Question 22

True or False: The graph of f(x) = 2^x passes through the point (0,1).

Answer 22

True

Question 23

What is the vertical intercept of the function f(x) = 2 * (3)^x?

Answer 23

2

Question 24

What is the impact of a negative exponent in an exponential function?

Answer 24

It reflects the function across the y-axis.

Question 25

True or False: The function f(x) = 1.5^(-x) represents exponential growth.

Answer 25

False

Question 26

Calculate f(3) for the function f(x) = 5 * (2)^x.

Answer 26

40

Question 27

What type of growth does the function f(x) = 10 * (1.5)^x exhibit?

Answer 27

Exponential growth

Question 28

Identify the base of the function f(x) = 7 * e^(2x).

Answer 28

e

Question 29

Fill in the blank: As x increases, the function f(x) = 0.5^x approaches __________.

Answer 29

0

Question 30

What is the effect of a coefficient in front of an exponential function?

Answer 30

It vertically stretches or compresses the graph.

Question 31

What does the base of an exponential function determine?

Answer 31

The rate of growth or decay.

Question 32

True or False: Exponential functions can model real-world phenomena such as population growth.

Answer 32

True