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Lesson: Base e Exponential Equations

Worksheet • 5 Questions

Q1:

Solve 3 𝑒 βˆ’ 4 = 8 π‘₯ , giving your answer correct to three decimal places.

  • A π‘₯ = 1 . 3 8 6
  • B π‘₯ = 0 . 9 8 1
  • C π‘₯ = 0 . 2 8 8
  • D π‘₯ = 1 . 9 4 6
  • E π‘₯ = 2 . 4 8 5

Q2:

Find, to the nearest thousandth, the value of π‘₯ such that 𝑒 = 1 9 4 π‘₯ βˆ’ 3 .

Q3:

Solve 2 = 5 𝑒 π‘₯ π‘₯ βˆ’ 1 for π‘₯ , giving your answer to three decimal places.

  • A π‘₯ = βˆ’ 1 . 9 8 6
  • B π‘₯ = βˆ’ 1 . 4 6 4
  • C π‘₯ = 1 . 9 8 6
  • D π‘₯ = 1 . 7 5 6
  • E π‘₯ = 1 . 4 6 4

Q4:

Consider the function 𝑓 ( π‘₯ ) = 4 𝑒 βˆ’ 1 2 𝑒 + 1   .

How many solutions does the equation 𝑓 ( π‘₯ ) = βˆ’ 2 have?

  • A1
  • B0
  • C2

How many solutions does the equation 𝑓 ( π‘₯ ) = 1 have?

  • A0
  • B1
  • C2

How many solutions does the equation 𝑓 ( π‘₯ ) = 4 have?

  • A1
  • B0
  • C2

What is the range of the function 𝑓 ( π‘₯ ) ?

  • A βˆ’ 1 < 𝑦 < 2
  • B βˆ’ 2 . 5 < 𝑦 < 3
  • C βˆ’ ∞ < 𝑦 < 2
  • D 2 < 𝑦 < ∞
  • E 0 < 𝑦 < 2

Q5:

Consider the function 𝑓 ( π‘₯ ) = 4 𝑒 βˆ’ 1 3 𝑒 + 1   .

How many solutions does the equation 𝑓 ( π‘₯ ) = βˆ’ 3 2 have?

  • A1
  • B0
  • C2

What is the range of the function 𝑓 ( π‘₯ ) ?

  • A βˆ’ 1 < 𝑦 < 4 3
  • B βˆ’ 1 < 𝑦 < 3
  • C βˆ’ 1 . 5 < 𝑦 < ∞
  • D 0 < 𝑦 < 4
  • E 1 < 𝑦 < 4 3
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