Deck 6: Logarithmic Links: Logarithmic and Exponential Functions

Question 1

Find a value for a to make the inequality true:

Answer 1

3

Question 2

Expand the following expression using rules of logarithms:

Answer 2

Question 3

Expand the following expression using rules of logarithms:

A)
B)
C)
D)

Answer 3

Question 4

Contract the following expression using rules of logarithms. Express your answer as a single logarithm.

Question 5

Contract the following expression using rules of logarithms. Express your answer as a single logarithm.

A)
B)
C)
D)

Question 6

Expand the following expression using rules of logarithms:

Question 7

Expand the following expression using rules of logarithms:

A)
B)
C)
D)

Question 8

Contract the following expression using rules of logarithms. Express your answer as a single logarithm.

Question 9

Contract the following expression using rules of logarithms. Express your answer as a single logarithm.

A)
B)
C)
D)

Question 10

Expand the following expression using rules of logarithms:

Question 11

Expand the following expression using rules of logarithms:

A)
B)
C)
D)

Question 12

Contract the following expression using rules of logarithms. Express your answer as a single logarithm.

Question 13

Contract the following expression using rules of logarithms. Express your answer as a single logarithm.

A)
B)
C)
D)

Question 14

Expand the following expression using rules of logarithms:

Question 15

Expand the following expression using rules of logarithms:

A)
B)
C)
D)

Question 16

Contract the following expression using rules of logarithms. Write your answer as a single logarithm.

Question 17

Contract the following expression using rules of logarithms. Write your answer as a single logarithm.

A)
B)
C)
D)

Question 18

Expand the following expression using rules of logarithms:

Question 19

Expand the following expression using rules of logarithms:

A)
B)
C)
D)

Question 20

Contract the following expression using rules of logarithms. Write your answer as a single logarithm.

Question 21

Contract the following expression using rules of logarithms. Write your answer as a single logarithm.

A)
B)
C)
D)

Question 22

Solve the equation for t.

Round your answer to 2 decimal places.

Question 23

Which of the following is the exact solution to the equation?

A)
B)
C)
D)

Question 24

The function, , gives the value, V, of an investment t years after the initial investment. How many years until the investment is worth $420,000?
Round your answer to the nearest year.

Question 25

The function, , gives the value, V, of an investment t years after the initial investment. How many years until the value of the investment doubles?
Round your answer to the nearest year.

Question 26

Upon her retirement, Mary begins to receive money from a retirement account. The function, , gives the money remaining, M, in the account t years after her retirement. How many years until the account balance is $490,000?
Round your answer to the nearest year.

Question 27

Upon her retirement, Mary begins to receive money from a retirement account. The function, , gives the money remaining, M, in the account t years after her retirement. How many years until Mary has received half of the money from the account?
Round your answer to the nearest year.

Question 28

The number of people, N, visiting a particular web site increases 10% each week. If the web site had 90,000 visitors this week, how many weeks until the number of people reaches 340,000?
Round your answer to the nearest week.

Question 29

The number of people, N, visiting a particular web site increases 8% each week. If the web site had 20,000 visitors this week, how many weeks until the number of people doubles?
Round your answer to the nearest week.

Question 30

Radium-226 has a half-life of 1600 years. If a fossil has 44% of it's original Radium-226 left, how old is it?
Round your answer to the nearest tenth of a year.

Question 31

Solve the equation for x.

Question 32

Solve the equation for x.

Round your answer to 2 decimal places.

Question 33

Which of the following is the exact solution of the equation?

A)
B)
C)
D)

Question 34

Solve the equation for x.

Round your answer to 2 decimal places.

Question 35

Which of the following is the exact solution of the equation?

A)
B)
C)
D)

Question 36

Solve the equation for x.

Round your answer to 2 decimal places.

Question 37

Which of the following is the exact solution of the equation?

A)
B)
C)
D)

Question 38

Expand the following expression using rules of logarithms:

Question 39

Expand the following expression using rules of logarithms:

A)
B)
C)
D)

Question 40

Contract the following expression using rules of logarithms. Express your answer as a single logarithm.

Question 41

Contract the following expression using rules of logarithms. Express your answer as a single logarithm.

A)
B)
C)
D)

Question 42

Expand the following expression using rules of logarithms:

Question 43

Expand the following expression using rules of logarithms:

A)
B)
C)
D)

Question 44

Contract the following expression using rules of logarithms. Express your answer as a single logarithm.

Question 45

Contract the following expression using rules of logarithms. Express your answer as a single logarithm.

A)
B)
C)
D)

Question 46

Expand the following expression using rules of logarithms:

Question 47

Expand the following expression using rules of logarithms:

A)
B)
C)
D)

Question 48

Contract the following expression using rules of logarithms. Express your answer as a single logarithm.

Question 49

Contract the following expression using rules of logarithms. Express your answer as a single logarithm.

A)
B)
C)
D)

Question 50

Expand the following expression using rules of logarithms:

Question 51

Expand the following expression using rules of logarithms:

A)
B)
C)
D)

Question 52

Contract the following expression using rules of logarithms. Write your answer as a single logarithm.

Question 53

Contract the following expression using rules of logarithms. Write your answer as a single logarithm.

A)
B)
C)
D)

Question 54

Expand the following expression using rules of logarithms:

Question 55

Expand the following expression using rules of logarithms:

A)
B)
C)
D)

Question 56

Contract the following expression using rules of logarithms. Write your answer as a single logarithm.

Question 57

Contract the following expression using rules of logarithms. Write your answer as a single logarithm.

A)
B)
C)
D)

Question 58

Solve the equation for t.

Round your answer to 2 decimal places.

Question 59

Which of the following is the exact solution to the equation:

A)
B)
C)
D)

Question 60

Solve the equation for t.

Round your answer to 2 decimal places.

Question 61

Which of the following is the exact solution to the equation:

A)
B)
C)
D)

Question 62

The function, , gives the value, V, of an investment t years after the initial investment. How many years until the investment is worth $1,200?
Round your answer to the nearest year.

Question 63

The function, , gives the value, V, of an investment t years after the initial investment. How many years until the worth of the investment doubles?
Round your answer to the nearest year.

Question 64

Upon her retirement, Mary begins to receive money from a retirement account. The function, , gives the money remaining, M, in the account t years after her retirement. How many years until the account balance is $360,000?
Round your answer to the nearest year.

Question 65

Upon her retirement, Mary begins to receive money from a retirement account. The function, , gives the money remaining, M, in the account t years after her retirement. How many years until Mary has received half of the money from the account?
Round your answer to the nearest year.

Question 66

Radium-226 has a half-life of 1600 years.

A) Find the continuous decay rate. Write your answer as a percent rounded 4 decimal places.
B) Then find the age of a fossil that has 67% of it's original Radium-226 left?Round your answer to the nearest year.

Question 67

Solve the equation for x.

Round your answer to 2 decimal places.

Question 68

Which of the following is the exact solution of the equation?

A)
B)
C)
D)

Question 69

Solve the equation for x.

Round your answer to 2 decimal places.

Question 70

Which of the following is the exact solution of the equation?

A)
B)
C)
D)

Question 71

Solve the equation for x.

Round your answer to 2 decimal places.

Question 72

Which of the following is the exact solution of the equation?

A)
B)
C)
D)

Question 73

Solve the equation for x.

Round your answer to 2 decimal places.

Question 74

Which of the following is the exact solution of the equation?

A)
B)
C)
D)

Question 75

The population of a town grew from 10,000 in 1999 to 12,000 in 2003. Find A) the annual growth rate and B) the continuou growth rate.
Write your answer as a percent rounded to 2 decimal places, like 13.45%.

Question 76

The population of a town grew from 9,000 in 1996 to 13,000 in 1999.

A) Find a function of the form, , for the population, P, of the town as a function of t, the number of years after 1996.Round values to 2 decimal places.
B) Use this function to find the population in 2005.Round your answer to the nearest person.

Question 77

Find k by converting a to .

Round your answer to 2 decimal places.

Question 78

Find A) the continuous growth factor and B) the (annual) growth factor from the function,
Write your answers as percents rounded to 2 decimal places, like 23.75%.

Question 79

A growth rate of 14% of corresponds to what continuous growth rate?
Write your answer as a percent rounded to 2 decimal places.

Question 80

A continuous growth rate of 49% of corresponds to what growth rate?
Write your answer as a percent rounded to 2 decimal places.