# 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 , where is the price of the car after years, determine the price of the car after 7 years. Give your answer correct to two decimal places.

Q2:

Given that , determine the value of .

• A
• B
• C
• D

Q3:

Complete the given table of function values for an exponential function with and .

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

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

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

What parameter in the formula determines this factor, or ?

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

Q4:

Given that and , determine the value of .

Q5:

If , what is ?

Q6:

Consider an exponential function .

Give an expression for .

• A
• B
• C
• D
• E

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

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

Q7:

Given that , determine .

Q8:

Given that , determine the value of .

• A
• B
• C
• D

Q9:

Given that , determine the value of .

• A
• B
• C81
• D

Q10:

The magnitude of an earthquake on the Richter scale is given by , where is the intensity of the earthquake and is a fixed reference intensity. What is the magnitude of an earthquake whose intensity is times the reference intensity?

Q11:

Given that , determine the value of .

• A
• B
• C5
• D

Q12:

Determine the value of given that .

• A
• B
• C
• D

Q13:

Given that the market price of a car decreases according to the relation , where is the price of the car in pounds, and is the time in years since the date of purchase, determine the price of the car when it was brand new.

Q14:

Given that , find the value of .

• A
• B
• C
• D
• E

Q15:

Given that , determine the value of .

• A
• B
• C
• D

Q16:

Find the value of , where and .

Q17:

Given that , determine the value of .

• A
• B
• C
• D

Q18:

Given that , which of the choices below is equal to ?

• A
• B
• C
• D

Q19:

Explain why the function is not exponential.

• Athe exponent
• Bthe base
• Cthe base
• Dthe exponent

Q20:

Given that , determine the value of .

• A
• B
• C
• D 216
• E 18