Worksheet: Exponential Functions

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

Q1:

Write an exponential equation in the form 𝑦=𝑏 for the numbers in the table.

π‘₯245
𝑦916812562431,024
  • A𝑦=ο€Ό34οˆο—
  • B𝑦=ο€Ό916οˆο—
  • C𝑦=ο€Ό932οˆο—
  • D𝑦=(π‘₯)οŽ₯
  • E𝑦=(π‘₯)

Q2:

Write an exponential equation in the form 𝑦=π‘Ž(𝑏) for the numbers in the table.

π‘₯0123
𝑦186223
  • A𝑦=2(3)
  • B𝑦=18ο€Ό13οˆο—
  • C𝑦=3(2)
  • D𝑦=13(18)
  • E𝑦=2π‘₯

Q3:

The curve below is 𝑦=π΄βˆ’π΅(1βˆ’π‘)οŠ±ο— for positive constants 𝐴, 𝐡, and 𝑏. Determine these, in that order, using the information in the figure.

  • A𝐴=15, 𝐡=10, 𝑏=√2
  • B𝐴=15, 𝐡=4, 𝑏=4
  • C𝐴=10, 𝐡=5, 𝑏=16
  • D𝐴=15, 𝐡=6, 𝑏=2
  • E𝐴=10, 𝐡=5, 𝑏=√2

Q4:

An initial bacteria population π‘ƒοŠ¦ doubles every hour, which is described by the formula 𝑃=𝑃⋅2οŠ¦ο‚. Write 𝑃 in the form 𝑃=π‘ƒβ‹…π‘οŠ¦ο»οŽ‘οŽ£ stating 𝑏 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.

  • A𝑃=ο€Ή1.7β‹…10ο…οŠ­ο»οŽ‘οŽ£, the bacteria population is multiplied by 1.7β‹…10 every day
  • B𝑃=𝑃⋅1.7β‹…10ο…οŠ¦οŠ­ο‚, the bacteria population is multiplied by 1.7β‹…10 every hour
  • C𝑃=𝑃⋅1.7β‹…10ο…οŠ¦οŠ­ο»οŽ‘οŽ£, the bacteria population is multiplied by 1.7β‹…10 every day
  • D𝑃=𝑃⋅(2), the bacteria population is multiplied by 2 every day
  • E𝑃=𝑃⋅1.7β‹…10ο…οŠ¦οŠ­οŽ οŽ‘οŽ£, the bacteria population is multiplied by 1.7β‹…10 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 45,000 listeners. Write an equation that can be used to calculate 𝐿, the number of listeners they expect to have in 𝑑 years’ time.

  • A𝐿=45,000(0.005)
  • B𝐿=45,000(0.995)
  • C𝐿=45,000(0.995)ο‘‰οŽ οŽ‘
  • D𝐿=45,000(1.005)
  • E𝐿=45,000(1.005)ο‘‰οŽ οŽ‘

Q6:

Write an equation in the form 𝑦=π‘Ž(𝑏) for the numbers in the table.

π‘₯134
𝑦246βˆ’3
  • A𝑦=βˆ’48ο€Όβˆ’12οˆο—
  • B𝑦=48ο€Ό12οˆο—
  • C𝑦=12(2)
  • D𝑦=12π‘₯
  • E𝑦=βˆ’12(βˆ’2)

Q7:

Write an exponential equation in the form 𝑦=𝑏 for the numbers in the table.

π‘₯0123
𝑦1525125
  • A𝑦=π‘₯
  • B𝑦=25
  • C𝑦=5
  • D𝑦=5οŠ«ο—
  • E𝑦=π‘₯

Q8:

Write an exponential equation in the form 𝑦=π‘Ž(𝑏) for the numbers in the table.

π‘₯0123
π‘¦βˆ’2βˆ’10βˆ’50βˆ’250
  • A𝑦=2(βˆ’5)
  • B𝑦=5(βˆ’2)
  • C𝑦=βˆ’2π‘₯
  • D𝑦=βˆ’5(2)
  • E𝑦=βˆ’2(5)

Q9:

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

Find the 𝑦-intercept in the shown graph.

As this graph represents an exponential function, every 𝑦-value is multiplied by 𝑏 when π‘₯ increases by Ξ”π‘₯. Find 𝑏 for Ξ”π‘₯=1.

Find the equation that describes the graph in the form 𝑦=π‘Žπ‘ο‘ο«ο‘.

  • A𝑦=10β‹…2
  • B𝑦=2
  • C𝑦=10β‹…ο€Ό14οˆο—
  • D𝑦=10β‹…ο€Ό12οˆο—
  • E𝑦=10β‹…4

Q10:

The given graph shows that 𝑦=𝑓(π‘₯).

Write an explicit formula for 𝑓(π‘₯) in the form 𝑓(π‘₯)=π‘Žπ‘ο‘οŽ’.

  • A𝑓(π‘₯)=2β‹…2οŽ’ο‘
  • B𝑓(π‘₯)=2β‹…2
  • C𝑓(π‘₯)=3β‹…2ο‘οŽ‘
  • D𝑓(π‘₯)=2β‹…2ο‘οŽ’
  • E𝑓(π‘₯)=2β‹…3ο‘οŽ‘

Graphically estimate the number that 𝑦 is multiplied by when π‘₯ increases by 1.

What calculation would allow you to find an accurate value for 𝑏 if you wanted to write 𝑓(π‘₯) in the form 𝑓(π‘₯)=π‘Žπ‘ο—?

  • A2=√2
  • B2=√2
  • C3=√3

Q11:

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

Find the 𝑦-intercept in the shown graph.

As this graph represents an exponential function, every 𝑦-value is multiplied by 𝑏 when π‘₯ increases by Ξ”π‘₯. Find 𝑏 for Ξ”π‘₯=1.

  • A13
  • B2
  • C4
  • D12
  • E14

Find the equation that describes the graph in the form 𝑦=π‘Žπ‘ο‘ο«ο‘.

  • A𝑦=4β‹…ο€Ό1400οˆο—
  • B𝑦=400β‹…ο€Ό12οˆο—
  • C𝑦=400β‹…ο€Ό14οˆο—
  • D𝑦=400β‹…π‘₯οŠͺ
  • E𝑦=400β‹…ο€Ό13οˆο—

Q12:

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

Find the 𝑦-intercept in the shown graph.

As this graph represents an exponential function, every 𝑦-value is multiplied by 𝑏 when π‘₯ increases by Ξ”π‘₯. Find 𝑏 for Ξ”π‘₯=3.

  • A14
  • B4
  • C13
  • D5
  • E15

Find the equation that describes the graph in the form 𝑦=π‘Žπ‘ο‘ο«ο‘.

  • A𝑦=2,500β‹…ο€Ό14οˆο‘οŽ‘
  • B𝑦=2,500β‹…ο€Ό12οˆο‘οŽ£
  • C𝑦=2,500β‹…ο€Ό15οˆο‘οŽ’
  • D𝑦=2,500β‹…ο€Ό15οˆοŠ©ο—
  • E𝑦=2,500β‹…ο€Ό15οˆο—

Q13:

The given graph shows that 𝑦=𝑓(π‘₯).

Write an explicit formula for 𝑓(π‘₯) in the form 𝑓(π‘₯)=π‘Žπ‘ο‘οŽ€.

  • A𝑓(π‘₯)=6β‹…ο€Ό13οˆο‘οŽ€
  • B𝑓(π‘₯)=6β‹…ο€Ό13οˆοŠ«ο—
  • C𝑓(π‘₯)=6β‹…ο€Ό15οˆο‘οŽ’
  • D𝑓(π‘₯)=6β‹…3ο‘οŽ€
  • E𝑓(π‘₯)=6β‹…ο€Ό13οˆο—

Graphically estimate the number that 𝑦 is multiplied by when π‘₯ increases by 1.

  • A3
  • B4.9
  • C0.03
  • D0.3
  • E0.8

What calculation would allow you to find an accurate value for 𝑏 if you wanted to write 𝑓(π‘₯) in the form 𝑓(π‘₯)=π‘Žπ‘ο—?

  • A(3)=√3
  • Bο€Ό15=ο„ž15
  • C(5)=√5
  • Dο€Ό13=ο„ž13
  • E(3)=243

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 𝑑 hours?

  • A3(5)
  • B5(2)
  • C5(3)
  • D15
  • E5(𝑑)

Q15:

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

Write an equation to represent the statement β€œTo calculate the value of 𝑦, increase π‘₯ by 13%.”

  • A𝑦=1.013π‘₯
  • B𝑦=1.13π‘₯
  • C𝑦=0.87π‘₯
  • D𝑦=0.13π‘₯
  • E𝑦=13π‘₯

A company aims to increase its profits by 13% every year for the next 3 years. If its profit this year is π‘ƒοŠ¦, write an equation to calculate π‘ƒοŠ©, the profit in 3 years’ time.

  • A𝑃=𝑃(1.13)
  • B𝑃=𝑃(1.013)
  • C𝑃=𝑃(13)
  • D𝑃=𝑃(0.13)
  • E𝑃=𝑃(0.87)

Q16:

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

Write an equation to represent the statement β€œTo calculate the value of 𝑦, decrease π‘₯ by 5%.”

  • A𝑦=1.05π‘₯
  • B𝑦=1.5π‘₯
  • C𝑦=0.05π‘₯
  • D𝑦=0.95π‘₯
  • E𝑦=0.5π‘₯

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 π‘Š, the amount they aim to produce in 𝑑 years .

  • Aπ‘Š=45(0.05)
  • Bπ‘Š=45(1.5)
  • Cπ‘Š=45(0.5)
  • Dπ‘Š=45(1.05)
  • Eπ‘Š=45(0.95)

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, 𝐴, 𝑑 years after it was purchased.

  • A𝐴=600(0.96)
  • B𝐴=600(4)
  • C𝐴=600(1.04)
  • D𝐴=600(0.04)
  • E𝐴=600(1.4)

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 𝑑 years and makes no other deposits or withdrawals.

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

  • A𝑉=450(0.93)
  • B𝑉=450(1.07)
  • C𝑉=450(0.07)
  • D𝑉=450(𝑑)οŠ¦οŽ–οŠ―οŠ©
  • E𝑉=450(𝑑)οŠ§οŽ–οŠ¦οŠ­

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 $1,020, find, to the nearest dollar, her initial deposit.

Q19:

David wants to invest his savings. He has found a fund which pays 7% a year, compounded annually. He would like to have $12,000 in that fund after 3 years. Write an equation that can be used to find 𝑃, the amount in dollars that David must invest for him to have $12,000 in the fund after 3 years.

  • A𝑃=120(0.07)
  • B𝑃(1.07)=12,000
  • C𝑃=120(1.07)
  • D𝑃=12,000(1.07)
  • E𝑃(0.07)=12,000

Q20:

Write an exponential equation in the form 𝑦=π‘Ž(𝑏) for the numbers in the table.

π‘₯0123
𝑦51545135
  • A𝑦=3π‘₯
  • B𝑦=5(3)
  • C𝑦=5π‘₯
  • D𝑦=3(5)
  • E𝑦=15

Q21:

Write an equation in the form 𝑦=π‘Ž(𝑏) for the numbers in the table.

π‘₯0123
π‘¦βˆ’46βˆ’913.5
  • A𝑦=βˆ’1.5(βˆ’4)
  • B𝑦=βˆ’4π‘₯οŠ±οŠ§οŽ–οŠ«
  • C𝑦=βˆ’4(βˆ’1.5)
  • D𝑦=4(βˆ’1.5)
  • E𝑦=βˆ’1.5(4)

Q22:

Write an equation to represent the statement β€œThe value of 𝑦 is equal to five to the power of π‘₯.”

  • A𝑦=π‘₯
  • B𝑦=5
  • C𝑦=π‘₯οŠ«ο—
  • D𝑦=5οŠ«ο—
  • E𝑦=5π‘₯

Q23:

Write an exponential equation in the form 𝑦=π‘Ž(𝑏) for the numbers in the table.

π‘₯123
𝑦4316156475
  • A𝑦=1615ο€Ό54οˆο—
  • B𝑦=53ο€Ό45οˆο—
  • C𝑦=54ο€Ό1615οˆο—
  • D𝑦=53ο€Ό54οˆο—
  • E𝑦=45ο€Ό53οˆο—

Q24:

Write an exponential equation in the form 𝑦=𝑏 for the numbers in the table.

π‘₯0123
𝑦1254258125
  • A𝑦=ο€Ό225οˆο—
  • B𝑦=ο€Ό25οˆο—
  • C𝑦=(π‘₯)
  • D𝑦=ο€Ό425οˆο—
  • E𝑦=(π‘₯)

Q25:

Write an equation to represent the statement β€œWhen 1.5 is raised to the power of π‘₯ and the result is multiplied by 4, the answer is 𝑦.”

  • A𝑦=4(π‘₯)οŠ§οŽ–οŠ«
  • B𝑦=1.5(4)
  • C𝑦=6
  • D𝑦=4(1.5)
  • E𝑦=1.5(π‘₯)οŠͺ

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.