# Lesson Worksheet: Exponential Functions Mathematics

In this worksheet, we will practice identifying, writing, evaluating, and analyzing exponential functions.

Q1:

Write an exponential equation in the form for the numbers in the table.

 𝑥 𝑦 2 4 5 916 81256 2431,024
• A
• B
• C
• D
• E

Q2:

Write an exponential equation in the form for the numbers in the table.

 𝑥 𝑦 0 1 2 3 18 6 2 23
• A
• B
• C
• D
• E

Q3:

Write an equation in the form for the numbers in the table.

 𝑥 𝑦 1 3 4 24 6 −3
• A
• B
• C
• D
• E

Q4:

Write an exponential equation in the form for the numbers in the table.

 𝑥 𝑦 0 1 2 3 1 5 25 125
• A
• B
• C
• D
• E

Q5:

Write an exponential equation in the form for the numbers in the table.

 𝑥 𝑦 0 1 2 3 −2 −10 −50 −250
• A
• B
• C
• D
• E

Q6:

Observe the given graph, and then answer the following questions.

Find the -intercept in the shown graph. As this graph represents an exponential function, every -value is multiplied by when increases by . Find for .

Find the equation that describes the graph in the form .

• A
• B
• C
• D
• E

Q7:

The given graph shows that .

Write an explicit formula for in the form . • A
• B
• C
• D
• E

Graphically estimate the number that is multiplied by when increases by 1.

• A3
• B4.9
• C0.03
• D0.3
• E0.8

What calculation would allow you to find an accurate value for if you wanted to write in the form ?

• A
• B
• C
• D
• E

Q8:

Write an exponential equation in the form for the numbers in the table.

 𝑥 𝑦 0 1 2 3 5 15 45 135
• A
• B
• C
• D
• E

Q9:

Write an equation in the form for the numbers in the table.

 𝑥 𝑦 0 1 2 3 −4 6 −9 13.5
• A
• B
• C
• D
• E

Q10:

Write an equation to represent the statement “The value of is equal to five to the power of .

• A
• B
• C
• D
• E

Q11:

Write an exponential equation in the form for the numbers in the table.

 𝑥 𝑦 1 2 3 43 1615 6475
• A
• B
• C
• D
• E

Q12:

Write an exponential equation in the form for the numbers in the table.

 𝑥 𝑦 0 1 2 3 1 25 425 8125
• A
• B
• C
• D
• E

Q13:

Write an equation to represent the statement “When 1.5 is raised to the power of and the result is multiplied by 4, the answer is .

• A
• B
• C
• D
• E

Q14:

Write an equation in the form for the numbers in the table.

 𝑥 𝑦 0 1 2 3 1 −2 4 −8
• A
• B
• C
• D
• E

Q15:

Write an equation in the form for the numbers in the table.

 𝑥 𝑦 1 2 4 −3 9 81
• A
• B
• C
• D
• E

Q16:

Write an exponential equation in the form for the numbers in the table.

 𝑥 𝑦 1 2 3 15 25 1253
• A
• B
• C
• D
• E

Q17:

What are the base and exponent of the function ?

• Abase , exponent
• Bbase , exponent
• Cbase , exponent
• Dbase , exponent

Q18:

Given that , determine the value of .

• A
• B
• C
• D

Q19:

Complete the given table of function values for an exponential function with and .

 𝑥 𝑦 −1 0 1 2
• A
 𝑥 𝑦 −1 0 1 2 0.5 1 2 4
• B
 𝑥 𝑦 −1 0 1 2 13 1 3 9
• C
 𝑥 𝑦 −1 0 1 2 1.5 3 6 12
• D
 𝑥 𝑦 −1 0 1 2 23 2 6 18
• E
 𝑥 𝑦 −1 0 1 2 3 0 3 12

How does this function grow (i.e., how does the -value change every time increases by 1)?

• AEvery time increases by 1, is multiplied by .
• BEvery time increases by 1, is multiplied by 3.
• CEvery time increases by 1, is multiplied by 2.
• DEvery time increases by 1, is multiplied by 1.
• EEvery time increases by 1, is multiplied by 6.

What parameter in the formula determines this factor, or ?

• AThe multiplication factor when increases by 1 is determined by .
• BThe multiplication factor when increases by 1 is determined by .

Q20:

Given that and , determine the value of .

Q21:

If , what is ?

Q22:

Consider an exponential function .

Give an expression for .

• A
• B
• C
• D
• E

What can you conclude about the way an exponential function grows?

• AAn exponential function grows by a constant factor over a constant interval .
• BAn exponential function grows by a constant factor over a constant interval .
• CAn exponential function grows by a constant factor over a constant interval .
• DAn exponential function grows by a constant factor over a constant interval .
• EAn exponential function grows by a constant factor over a constant interval .

Q23:

Given that , determine .

Q24:

Given that , determine the value of .

• A
• B
• C
• D

Q25:

Given that , determine the value of .

• A
• B81
• C
• D