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 ๐‘ฆ=๐‘๏— for the numbers in the table.

๐‘ฅ245
๐‘ฆ916812562431,024
  • A๐‘ฆ=๏€ผ34๏ˆ๏—
  • B๐‘ฆ=๏€ผ916๏ˆ๏—
  • C๐‘ฆ=๏€ผ932๏ˆ๏—
  • D๐‘ฆ=(๐‘ฅ)๏Žจ๏Ž ๏Žฅ
  • E๐‘ฆ=(๐‘ฅ)๏Žข๏Žฃ

Q2:

Write an exponential equation in the form ๐‘ฆ=๐‘Ž(๐‘)๏— for the numbers in the table.

๐‘ฅ0123
๐‘ฆ186223
  • A๐‘ฆ=2(3)๏—
  • B๐‘ฆ=18๏€ผ13๏ˆ๏—
  • C๐‘ฆ=3(2)๏—
  • D๐‘ฆ=13(18)๏—
  • E๐‘ฆ=2๐‘ฅ๏Šฉ

Q3:

Write an equation in the form ๐‘ฆ=๐‘Ž(๐‘)๏— for the numbers in the table.

๐‘ฅ134
๐‘ฆ246โˆ’3
  • A๐‘ฆ=โˆ’48๏€ผโˆ’12๏ˆ๏—
  • B๐‘ฆ=48๏€ผ12๏ˆ๏—
  • C๐‘ฆ=12(2)๏—
  • D๐‘ฆ=12๐‘ฅ๏Šจ
  • E๐‘ฆ=โˆ’12(โˆ’2)๏—

Q4:

Write an exponential equation in the form ๐‘ฆ=๐‘๏— for the numbers in the table.

๐‘ฅ0123
๐‘ฆ1525125
  • A๐‘ฆ=๐‘ฅ๏Šซ
  • B๐‘ฆ=25๏—
  • C๐‘ฆ=5๏—
  • D๐‘ฆ=5๏Šซ๏—
  • E๐‘ฆ=๐‘ฅ๏Šจ๏Šซ

Q5:

Write an exponential equation in the form ๐‘ฆ=๐‘Ž(๐‘)๏— for the numbers in the table.

๐‘ฅ0123
๐‘ฆโˆ’2โˆ’10โˆ’50โˆ’250
  • A๐‘ฆ=2(โˆ’5)๏—
  • B๐‘ฆ=5(โˆ’2)๏—
  • C๐‘ฆ=โˆ’2๐‘ฅ๏Šซ
  • D๐‘ฆ=โˆ’5(2)๏—
  • E๐‘ฆ=โˆ’2(5)๏—

Q6:

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

Find the ๐‘ฆ-intercept in the shown graph.

As this graph represents an exponential function, every ๐‘ฆ-value is multiplied by ๐‘ when ๐‘ฅ increases by ฮ”๐‘ฅ. Find ๐‘ for ฮ”๐‘ฅ=1.

Find the equation that describes the graph in the form ๐‘ฆ=๐‘Ž๐‘๏‘๏ซ๏‘.

  • A๐‘ฆ=10โ‹…2๏—
  • B๐‘ฆ=2๏—
  • C๐‘ฆ=10โ‹…๏€ผ14๏ˆ๏—
  • D๐‘ฆ=10โ‹…๏€ผ12๏ˆ๏—
  • E๐‘ฆ=10โ‹…4๏—

Q7:

The given graph shows that ๐‘ฆ=๐‘“(๐‘ฅ).

Write an explicit formula for ๐‘“(๐‘ฅ) in the form ๐‘“(๐‘ฅ)=๐‘Ž๐‘๏‘๏Žค.

  • A๐‘“(๐‘ฅ)=6โ‹…๏€ผ13๏ˆ๏‘๏Žค
  • B๐‘“(๐‘ฅ)=6โ‹…๏€ผ13๏ˆ๏Šซ๏—
  • C๐‘“(๐‘ฅ)=6โ‹…๏€ผ15๏ˆ๏‘๏Žข
  • D๐‘“(๐‘ฅ)=6โ‹…3๏‘๏Žค
  • E๐‘“(๐‘ฅ)=6โ‹…๏€ผ13๏ˆ๏—

Graphically estimate the number that ๐‘ฆ is multiplied by when ๐‘ฅ increases by 1.

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

What calculation would allow you to find an accurate value for ๐‘ if you wanted to write ๐‘“(๐‘ฅ) in the form ๐‘“(๐‘ฅ)=๐‘Ž๐‘๏—?

  • A(3)=โˆš3๏Ž ๏Žค๏Žค
  • B๏€ผ15๏ˆ=๏„ž15๏Ž ๏Žข๏Žข
  • C(5)=โˆš5๏Ž ๏Žข๏Žข
  • D๏€ผ13๏ˆ=๏„ž13๏Ž ๏Žค๏Žค
  • E(3)=243๏Šซ

Q8:

Write an exponential equation in the form ๐‘ฆ=๐‘Ž(๐‘)๏— for the numbers in the table.

๐‘ฅ0123
๐‘ฆ51545135
  • A๐‘ฆ=3๐‘ฅ๏Šซ
  • B๐‘ฆ=5(3)๏—
  • C๐‘ฆ=5๐‘ฅ๏Šฉ
  • D๐‘ฆ=3(5)๏—
  • E๐‘ฆ=15๏—

Q9:

Write an equation in the form ๐‘ฆ=๐‘Ž(๐‘)๏— for the numbers in the table.

๐‘ฅ0123
๐‘ฆโˆ’46โˆ’913.5
  • A๐‘ฆ=โˆ’1.5(โˆ’4)๏—
  • B๐‘ฆ=โˆ’4๐‘ฅ๏Šฑ๏Šง๏Ž–๏Šซ
  • C๐‘ฆ=โˆ’4(โˆ’1.5)๏—
  • D๐‘ฆ=4(โˆ’1.5)๏—
  • E๐‘ฆ=โˆ’1.5(4)๏—

Q10:

Write an equation to represent the statement โ€œThe value of ๐‘ฆ is equal to five to the power of ๐‘ฅ.โ€

  • A๐‘ฆ=๐‘ฅ๏Šซ
  • B๐‘ฆ=5๏—
  • C๐‘ฆ=๐‘ฅ๏Šซ๏—
  • D๐‘ฆ=5๏Šซ๏—
  • E๐‘ฆ=5๐‘ฅ

Q11:

Write an exponential equation in the form ๐‘ฆ=๐‘Ž(๐‘)๏— for the numbers in the table.

๐‘ฅ123
๐‘ฆ4316156475
  • A๐‘ฆ=1615๏€ผ54๏ˆ๏—
  • B๐‘ฆ=53๏€ผ45๏ˆ๏—
  • C๐‘ฆ=54๏€ผ1615๏ˆ๏—
  • D๐‘ฆ=53๏€ผ54๏ˆ๏—
  • E๐‘ฆ=45๏€ผ53๏ˆ๏—

Q12:

Write an exponential equation in the form ๐‘ฆ=๐‘๏— for the numbers in the table.

๐‘ฅ0123
๐‘ฆ1254258125
  • A๐‘ฆ=๏€ผ225๏ˆ๏—
  • B๐‘ฆ=๏€ผ25๏ˆ๏—
  • C๐‘ฆ=(๐‘ฅ)๏Žก๏Žก๏Žค
  • D๐‘ฆ=๏€ผ425๏ˆ๏—
  • E๐‘ฆ=(๐‘ฅ)๏Žก๏Žค

Q13:

Write an equation to represent the statement โ€œWhen 1.5 is raised to the power of ๐‘ฅ and the result is multiplied by 4, the answer is ๐‘ฆ.โ€

  • A๐‘ฆ=4(๐‘ฅ)๏Šง๏Ž–๏Šซ
  • B๐‘ฆ=1.5(4)๏—
  • C๐‘ฆ=6๏—
  • D๐‘ฆ=4(1.5)๏—
  • E๐‘ฆ=1.5(๐‘ฅ)๏Šช

Q14:

Write an equation in the form ๐‘ฆ=๐‘๏— for the numbers in the table.

๐‘ฅ0123
๐‘ฆ1โˆ’24โˆ’8
  • A๐‘ฆ=๐‘ฅ๏Šจ
  • B๐‘ฆ=โˆ’(2)๏—
  • C๐‘ฆ=(โˆ’2)๏—
  • D๐‘ฆ=2๏—
  • E๐‘ฆ=๐‘ฅ๏Šฑ๏Šจ

Q15:

Write an equation in the form ๐‘ฆ=๐‘๏— for the numbers in the table.

๐‘ฅ124
๐‘ฆโˆ’3981
  • A๐‘ฆ=(โˆ’3)๏—
  • B๐‘ฆ=โˆ’(3)๏—
  • C๐‘ฆ=๐‘ฅ๏Šฑ๏Šฉ
  • D๐‘ฆ=9๏—
  • E๐‘ฆ=๐‘ฅ๏Šฉ

Q16:

Write an exponential equation in the form ๐‘ฆ=๐‘Ž(๐‘)๏— for the numbers in the table.

๐‘ฅ123
๐‘ฆ15251253
  • A๐‘ฆ=53(9)๏—
  • B๐‘ฆ=35(25)๏—
  • C๐‘ฆ=25๏€ผ35๏ˆ๏—
  • D๐‘ฆ=53๐‘ฅ๏Šฏ
  • E๐‘ฆ=9๏€ผ53๏ˆ๏—

Q17:

What are the base and exponent of the function ๐‘“(๐‘ฅ)=5๏—๏Šฑ๏Šซ?

  • Abase =๐‘ฅโˆ’5, exponent =5
  • Bbase =5, exponent =๐‘ฅโˆ’5
  • Cbase =5, exponent =๐‘ฅ+5
  • Dbase =๐‘ฅ+5, exponent =5

Q18:

Given that ๐‘“(๐‘ฅ)=3๏—๏Šฑ๏Šฎ, determine the value of ๐‘“(๐‘ฅ+9).

  • A3๏—๏Šฐ๏Šง๏Šญ
  • B3๏Šจ๏—๏Šฐ๏Šง
  • C3๏—๏Šฐ๏Šง
  • D3๏Šจ๏—๏Šฐ๏Šง๏Šญ

Q19:

Complete the given table of function values for an exponential function ๐‘ฆ=๐‘Ž๐‘๏— with ๐‘Ž=3 and ๐‘=2.

๐‘ฅโˆ’1012
๐‘ฆ
  • A
    ๐‘ฅโˆ’1012
    ๐‘ฆ0.5124
  • B
    ๐‘ฅโˆ’1012
    ๐‘ฆ13139
  • C
    ๐‘ฅโˆ’1012
    ๐‘ฆ1.53612
  • D
    ๐‘ฅโˆ’1012
    ๐‘ฆ232618
  • E
    ๐‘ฅโˆ’1012
    ๐‘ฆ30312

How does this function grow (i.e., how does the ๐‘ฆ-value change every time ๐‘ฅ increases by 1)?

  • AEvery time ๐‘ฅ increases by 1, ๐‘ฆ is multiplied by โˆ’2.
  • BEvery time ๐‘ฅ increases by 1, ๐‘ฆ is multiplied by 3.
  • CEvery time ๐‘ฅ increases by 1, ๐‘ฆ is multiplied by 2.
  • DEvery time ๐‘ฅ increases by 1, ๐‘ฆ is multiplied by 1.
  • EEvery time ๐‘ฅ increases by 1, ๐‘ฆ is multiplied by 6.

What parameter in the formula ๐‘ฆ=๐‘Ž๐‘๏— determines this factor, ๐‘Ž or ๐‘?

  • AThe multiplication factor when ๐‘ฅ increases by 1 is determined by ๐‘.
  • BThe multiplication factor when ๐‘ฅ increases by 1 is determined by ๐‘Ž.

Q20:

Given that ๐‘“(๐‘ฅ)=8๏Šง๏— and ๐‘“(๐‘ฅ)=๏€ผ18๏ˆ๏Šจ๏—, determine the value of ๐‘“๏€ป๏‡โˆ’๐‘“(โˆ’4)๐‘“๏€ป๏‡โˆ’๐‘“(โˆ’2)๏Šง๏Šฏ๏Šจ๏Šจ๏Šง๏Šซ๏Šจ๏Šจ.

Q21:

If ๐‘“(๐‘ฅ)=90๏—, what is ๐‘“(๐‘ฅ)ร—๐‘“(โˆ’๐‘ฅ)?

Q22:

Consider an exponential function ๐‘“(๐‘ฅ)=๐‘Ž๐‘๏—.

Give an expression for ๐‘“(๐‘ฅ+ฮ”๐‘ฅ)๐‘“(๐‘ฅ).

  • A๐‘Ž๏‹ฒ๏—
  • B๐‘๏Šจ๏—๏Šฐ๏‹ฒ๏—
  • C๐‘๏—๏Šฑ๏‹ฒ๏—
  • D๐‘๏—๏Šฐ๏‹ฒ๏—
  • E๐‘๏‹ฒ๏—

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

  • AAn exponential function grows by a constant factor ๏€น๐‘Ž๏…๏‹ฒ๏— over a constant interval ฮ”๐‘ฅ.
  • BAn exponential function grows by a constant factor ๏€น๐‘๏…๏‹ฒ๏— over a constant interval ฮ”๐‘ฅ.
  • CAn exponential function grows by a constant factor ๏€น๐‘๏…๏—๏Šฐ๏‹ฒ๏— over a constant interval ฮ”๐‘ฅ.
  • DAn exponential function grows by a constant factor ๏€น๐‘๏…๏Šจ๏—๏Šฐ๏‹ฒ๏— over a constant interval ฮ”๐‘ฅ.
  • EAn exponential function grows by a constant factor ๏€น๐‘๏…๏—๏Šฑ๏‹ฒ๏— over a constant interval ฮ”๐‘ฅ.

Q23:

Given that ๐‘“(๐‘ฅ)=8๏—, determine ๐‘“(๐‘ฅ)ร—๐‘“(โˆ’๐‘ฅ).

Q24:

Given that ๐‘“(๐‘ฅ)=3๏—, determine the value of ๐‘“(3๐‘ฅ+2)+๐‘“(3๐‘ฅโˆ’1)9๐‘“(3๐‘ฅ)+7๐‘“(3๐‘ฅโˆ’1).

  • A1714
  • B57
  • C1417
  • D75

Q25:

Given that ๐‘“(๐‘ฅ)=9๏—, determine the value of ๐‘“(๐‘ฅ+7)+๐‘“(๐‘ฅ+5)๐‘“(๐‘ฅ+9)+๐‘“(๐‘ฅ+7).

  • Aโˆ’81
  • B81
  • Cโˆ’181
  • D181

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