# Lesson Worksheet: Exponential Functions Mathematics

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

**Q3: **

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

1 | 3 | 4 | |

24 | 6 |

- A
- B
- C
- D
- E

**Q5: **

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

0 | 1 | 2 | 3 | |

- 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
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- 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 ?

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- B
- C
- D
- E

**Q9: **

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

0 | 1 | 2 | 3 | |

6 | 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.

1 | 2 | 3 | |

- 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

**Q17: **

What are the base and exponent of the function ?

- Abase , exponent
- Bbase , exponent
- Cbase , exponent
- Dbase , exponent

**Q19: **

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

0 | 1 | 2 | ||

- A
0 1 2 0.5 1 2 4 - B
0 1 2 1 3 9 - C
0 1 2 1.5 3 6 12 - D
0 1 2 2 6 18 - E
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 .

**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