Worksheet: Evaluating Exponential Functions

In this worksheet, we will practice evaluating exponential functions.

Q1:

Given that the market price of a car decreases according to the formula 𝑥 = 1 7 0 , 0 0 0 ( 0 . 9 ) , where 𝑥 L E is the price of the car after 𝑛 years, determine the price of the car after 7 years. Give your answer correct to two decimal places.

Q2:

Given that 𝑓 ( 𝑥 ) = 3 , determine the value of 𝑓 ( 𝑥 + 9 ) .

  • A 3
  • B 3
  • C 3
  • D 3

Q3:

Complete the given table of function values for an exponential function 𝑦 = 𝑎 𝑏 with 𝑎 = 3 and 𝑏 = 2 .

𝑥 1 0 1 2
𝑦
  • A
    𝑥 1 0 1 2
    𝑦 3 0 3 12
  • B
    𝑥 1 0 1 2
    𝑦 2 3 2 6 18
  • C
    𝑥 1 0 1 2
    𝑦 1.5 3 6 12
  • D
    𝑥 1 0 1 2
    𝑦 1 3 1 3 9
  • E
    𝑥 1 0 1 2
    𝑦 0.5 1 2 4

How does this function grow (i.e., how does the 𝑦 -value change every time 𝑥 increases by 1)?

  • AEvery time 𝑥 increases by 1, 𝑦 is multiplied by 2 .
  • BEvery time 𝑥 increases by 1, 𝑦 is multiplied by 2.
  • CEvery time 𝑥 increases by 1, 𝑦 is multiplied by 1.
  • DEvery time 𝑥 increases by 1, 𝑦 is multiplied by 3.
  • EEvery time 𝑥 increases by 1, 𝑦 is multiplied by 6.

What parameter in the formula 𝑦 = 𝑎 𝑏 determines this factor, 𝑎 or 𝑏 ?

  • AThe multiplication factor when 𝑥 increases by 1 is determined by 𝑏 .
  • BThe multiplication factor when 𝑥 increases by 1 is determined by 𝑎 .

Q4:

Given that 𝑓 ( 𝑥 ) = 8 and 𝑓 ( 𝑥 ) = 1 8 , determine the value of 𝑓 𝑓 ( 4 ) 𝑓 𝑓 ( 2 ) .

Q5:

If 𝑓 ( 𝑥 ) = 9 0 , what is 𝑓 ( 𝑥 ) × 𝑓 ( 𝑥 ) ?

Q6:

Consider an exponential function 𝑓 ( 𝑥 ) = 𝑎 𝑏 .

Give an expression for 𝑓 ( 𝑥 + Δ 𝑥 ) 𝑓 ( 𝑥 ) .

  • A 𝑎
  • B 𝑏
  • C 𝑏
  • D 𝑏
  • E 𝑏

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

  • AAn exponential function grows by a constant factor 𝑏 over a constant interval Δ 𝑥 .
  • BAn exponential function grows by a constant factor 𝑏 over a constant interval Δ 𝑥 .
  • CAn exponential function grows by a constant factor 𝑏 over a constant interval Δ 𝑥 .
  • DAn exponential function grows by a constant factor 𝑎 over a constant interval Δ 𝑥 .
  • EAn exponential function grows by a constant factor 𝑏 over a constant interval Δ 𝑥 .

Q7:

Given that 𝑓 ( 𝑥 ) = 8 , determine 𝑓 ( 𝑥 ) × 𝑓 ( 𝑥 ) .

Q8:

Given that 𝑓 ( 𝑥 ) = 3 , determine the value of 𝑓 ( 3 𝑥 + 2 ) + 𝑓 ( 3 𝑥 1 ) 9 𝑓 ( 3 𝑥 ) + 7 𝑓 ( 3 𝑥 1 ) .

  • A 1 4 1 7
  • B 7 5
  • C 1 7 1 4
  • D 5 7

Q9:

Given that 𝑓 ( 𝑥 ) = 9 , determine the value of 𝑓 ( 𝑥 + 7 ) + 𝑓 ( 𝑥 + 5 ) 𝑓 ( 𝑥 + 9 ) + 𝑓 ( 𝑥 + 7 ) .

  • A 1 8 1
  • B 8 1
  • C81
  • D 1 8 1

Q10:

The magnitude of an earthquake on the Richter scale is given by 𝑀 ( 𝐼 ) = 𝐼 𝐼 l o g , where 𝐼 is the intensity of the earthquake and 𝐼 is a fixed reference intensity. What is the magnitude of an earthquake whose intensity is 1 0 times the reference intensity?

Q11:

Given that 𝑓 ( 𝑥 ) = 9 , determine the value of 𝑓 ( 𝑥 + 1 ) × 5 𝑓 ( 𝑥 ) 4 𝑓 ( 𝑥 1 ) × 𝑓 ( 𝑥 + 2 ) .

  • A 1 4
  • B 4 5
  • C5
  • D 5 4

Q12:

Determine the value of 𝑓 ( 𝑥 + 1 ) 𝑓 ( 𝑥 1 ) 𝑓 ( 𝑥 1 ) 𝑓 ( 𝑥 + 1 ) given that 𝑓 ( 𝑥 ) = 5 .

  • A 6 2 6 2 5
  • B 6 2 4 2 5
  • C 6 2 6 2 5
  • D 6 2 4 2 5

Q13:

Given that the market price of a car decreases according to the relation 𝑥 = 2 2 0 , 0 0 0 ( 0 . 3 9 ) , where 𝑥 is the price of the car in pounds, and 𝑛 is the time in years since the date of purchase, determine the price of the car when it was brand new.

Q14:

Given that 𝑓 ( 𝑥 ) = 𝑎 , find the value of 𝑓 ( 𝑥 + 1 1 ) + 𝑓 ( 𝑥 + 1 2 ) 𝑓 ( 𝑥 + 1 1 ) + 𝑓 ( 𝑥 + 1 0 ) .

  • A 1 5 𝑎
  • B 𝑎
  • C 𝑎
  • D 𝑎 + 1 2
  • E 1 5 𝑎 + 1 2

Q15:

Given that 𝑓 ( 𝑥 ) = 4 , determine the value of 𝑓 ( 𝑥 ) 𝑓 ( 𝑥 1 ) 𝑓 ( 𝑥 1 ) 𝑓 ( 𝑥 ) .

  • A 1 5 4
  • B 4 1 5
  • C 1 7 4
  • D 4 1 7

Q16:

Find the value of 𝑓 𝑓 ( 6 ) 𝑓 𝑓 ( 5 ) , where 𝑓 ( 𝑥 ) = 3 and 𝑓 ( 𝑥 ) = 1 3 .

Q17:

Given that 𝑓 ( 𝑥 ) = 2 , determine the value of 𝑓 ( 6 𝑥 + 9 ) 𝑓 ( 6 𝑥 + 8 ) 9 𝑓 ( 6 𝑥 + 6 ) 2 𝑓 ( 6 𝑥 + 4 ) .

  • A 1 6 3
  • B 8 1 7
  • C 1 4 6
  • D 1 2

Q18:

Given that 𝑓 ( 𝑥 ) = 4 , which of the choices below is equal to 4 𝑓 ( 𝑥 ) ?

  • A 4 𝑓 ( 𝑥 + 2 ) × 4 𝑓 ( 𝑥 + 3 ) 4 𝑓 ( 𝑥 + 4 )
  • B 𝑓 ( 𝑥 + 2 ) × 𝑓 ( 𝑥 + 3 ) 𝑓 ( 𝑥 + 4 )
  • C 4 𝑓 ( 𝑥 + 1 ) × 4 𝑓 ( 𝑥 + 2 ) 4 𝑓 ( 𝑥 + 3 )
  • D 𝑓 ( 𝑥 + 1 ) × 𝑓 ( 𝑥 + 2 ) 𝑓 ( 𝑥 + 3 )

Q19:

Explain why the function 𝑘 ( 𝑥 ) = 2 3 is not exponential.

  • Athe exponent 7 > 0
  • Bthe base 2 3 < 0
  • Cthe base 2 3 > 0
  • Dthe exponent 7 < 0

Q20:

Given that 𝑓 ( 𝑥 ) = 6 , determine the value of 𝑓 ( 3 ) .

  • A 1 1 8
  • B 2 1 6
  • C 1 2 1 6
  • D 216
  • E 18

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