# Worksheet: Writing Exponential Functions

In this worksheet, we will practice writing equivalent equations for exponential functions using tables of values, graphs, and descriptions.

**Q2: **

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

0 | 1 | 2 | 3 | |

18 | 6 | 2 |

- A
- B
- C
- D
- E

**Q3: **

The curve below is for positive constants , , and . Determine these, in that order, using the information in the figure.

- A , ,
- B , ,
- C , ,
- D , ,
- E , ,

**Q4: **

An initial bacteria population doubles every hour, which is described by the formula . Write in the form stating in scientific notation, to two significant figures, and find the number by which you would need to multiply the first days population to find the second.

- A , the bacteria population is multiplied by every hour
- B , the bacteria population is multiplied by every day
- C , the bacteria population is multiplied by every day
- D , the bacteria population is multiplied by every day
- E , the bacteria population is multiplied by 2 every day

**Q5: **

The producer of a successful radio show predicts that the number of listeners will increase by 0.5% a month. The show currently has listeners. Write an equation that can be used to calculate , the number of listeners they expect to have in yearsβ time.

- A
- B
- C
- D
- E

**Q6: **

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

1 | 3 | 4 | |

24 | 6 |

- A
- B
- C
- D
- E

**Q7: **

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

0 | 1 | 2 | 3 | |

1 | 5 | 25 | 125 |

- A
- B
- C
- D
- E

**Q8: **

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

0 | 1 | 2 | 3 | |

- A
- B
- C
- D
- E

**Q9: **

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

**Q10: **

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.

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

- A
- B
- C

**Q11: **

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 .

- A
- B4
- C
- D2
- E

Find the equation that describes the graph in the form .

- A
- B
- C
- D
- E

**Q12: **

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 βvalue is multiplied by when increases by . Find for .

- A
- B4
- C
- D
- E5

Find the equation that describes the graph in the form .

- A
- B
- C
- D
- E

**Q13: **

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.

- A0.8
- B0.03
- C0.3
- D4.9
- E3

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

- A
- B
- C
- D
- E

**Q14: **

The number of people who view a meme triples every hour. If 5 friends viewed a meme initially, how many people would have viewed it after one hour?

How many people would have viewed the meme after hours?

- A
- B
- C
- D
- E

**Q15: **

What must a number be multiplied by to increase it by 13%?

Write an equation to represent the statement βTo calculate the value of , increase by 13%.β

- A
- B
- C
- D
- E

A company aims to increase its profits by 13% every year for the next 3 years. If its profit this year is , write an equation to calculate , the profit in 3 yearsβ time.

- A
- B
- C
- D
- E

**Q16: **

What must a number be multiplied by to decrease it by 5%?

Write an equation to represent the statement βTo calculate the value of , decrease by 5%.β

- A
- B
- C
- D
- E

A manufacturer aims to decrease the amount of waste they produce by 5% every year. If they currently produce 45 tons of waste, write an equation to calculate , the amount they aim to produce in years .

- A
- B
- C
- D
- E

**Q17: **

Olivia bought an antique vase for $600. The value of the vase increases by 4% each year. Write an equation that can be used to find the value of the vase in dollars, , years after it was purchased.

- A
- B
- C
- D
- E

**Q18: **

Ethan decided to invest his savings in a high-interest account that pays 7% interest compounded annually. He invests $450 in the account for years and makes no other deposits or withdrawals.

Write an equation that can be used to calculate , the value of his investment in dollars after years.

- A
- B
- C
- D
- E

What will be the value of his investment after 7 years? Give your answer to the nearest dollar.

Emma invested her savings in the same account 5 years ago. She made no further deposits or withdrawals. If the balance in her account is now , find, to the nearest dollar, her initial deposit.

**Q19: **

David wants to invest his savings. He has found a fund which pays a year, compounded annually. He would like to have in that fund after 3 years. Write an equation that can be used to find , the amount in dollars that David must invest for him to have in the fund after 3 years.

- A
- B
- C
- D
- E

**Q20: **

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

0 | 1 | 2 | 3 | |

5 | 15 | 45 | 135 |

- A
- B
- C
- D
- E

**Q21: **

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

0 | 1 | 2 | 3 | |

6 | 13.5 |

- A
- B
- C
- D
- E

**Q22: **

Write an equation to represent the statement βThe value of is equal to five to the power of .β

- A
- B
- C
- D
- E

**Q23: **

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

1 | 2 | 3 | |

- A
- B
- C
- D
- E

**Q24: **

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

0 | 1 | 2 | 3 | |

1 |

- A
- B
- C
- D
- E

**Q25: **

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

- A
- B
- C
- D
- E