Deck 5: Logarithmic Functions

Question 1

By what order of magnitude do the numbers 0.0001 and 1,000,000 differ?

Answer 1

10

Question 2

If you wished to graph the number of moons of each planet in the solar system on a standard sheet of paper, would you use a standard or a logarithmic scale?

Answer 2

standard

Question 3

The following table gives z as a linear function of x.
If
, which of the following is a formula for y in terms of x?

A)
B)
C)
D)

Answer 3

Question 4

The following table gives z as a linear function of x.
If
, which of the following is a formula for y in terms of x?

A)
B)
C)
D)

Question 5

The following table gives z as a linear function of x.
If , find a formula for y in terms of x.

Question 6

The following table gives z as a linear function of x.
If and , find a formula for y in terms of x.

Question 7

The following table gives w as a linear function of u.
If , find at
.

Question 8

The following table gives v as a linear function of w.
If
and
, which of the following is a formula for y in terms of x?

A)
B)
C)
D)

Question 9

The following table gives v as a linear function of w. If and , find a formula for y in terms of x.

Question 10

The following table gives v as a linear function of w.
If

Question 11

The following table gives v as a linear function of w.
If
find a formula for y in terms of x.

Question 12

The following table gives v as a linear function of w.
If and , find a formula for y in terms of x.

Question 13

Use linear regression on the values t and
to fit a function of the form
.
Use a calculator program to find the slope of the regression line for this data. Round to 4 decimal places.

Question 14

The table below gives the number of ants living in a museum display. Use linear regression on the values t and
to fit a function of the form

.
Use a calculator program to find the regression line for this data. Use the regression line to calculate the number of ants after 22 months. Give your answer to the nearest whole number.

Question 15

Use linear regression on the values x and to fit a function of the form .
Use a calculator program to find the slope of the regression line for this data. Round to 4 decimal places.

Question 16

Use linear regression on the values x and to fit a function of the form .
Use a calculator program to find the regression line for this data. Use the regression line to find the y-value when x=53 . Give your answer correct to 2 decimal places.

Question 17

Use linear regression on the values x and to fit a function of the form . Use a calculator program to find the regression line for this data. Convert to an exponential function and give the value of k. Round to 4 decimal places.

Question 18

Use linear regression on the values x and to fit a function of the form .
Use a calculator program to find the slope of the regression line for this data. Round to 4 decimal places.

Question 19

Use linear regression on the values x and
to fit a function of the form .
Use a calculator program to find the regression line for this data. Convert to an exponential function . Give the value of k. Round to 4 decimal places.

Question 20

Use linear regression on the values x and
to fit a function of the form .
Use a calculator program to find the regression line for this data. Use the regression line to find the value of y when
. Round to 2 decimal places.

Question 21

What is the domain of the function ?

A)
B)
C)
D)

Question 22

The following figure shows the graphs of
(A).

(B).

(C).

(D).

.
Which one is the graph of C?

Question 23

The horizontal asymptote of the graph of is at y = _____. If necessary, round to 2 decimal places.

Question 24

The vertical asymptote of the graph of is at x = _____. Round to 2 decimal places if necessary.

Question 25

Let .

A) Graph f.
B) What are the asymptotes?
C) What are the intercepts?

Question 26

Solve for . Give your answer to 4 decimal places.

Question 27

Solve for t: . Round your answer to 3 decimal places.

Question 28

What is the hydrogen ion concentration [H⁺] for a substance with a pH of 4.3?

Question 29

Sound A is 31 dB. Sound B is 62 dB. How many times more intense is Sound B than Sound A?

Question 30

How many times more powerful is an earthquake measuring 5.3 on the Richter scale than an earthquake measuring 4.2 on the Richter scale? Round your answer to two decimal places.

Question 31

Find a possible formula for the following graph using either logarithms or exponentials.

Question 32

Find the domain of the function

.

Question 33

Find the domain of the function

.

Question 34

Consider the function

A) Graph the function.
B) State the domain.
C) State all asymptotes.

Question 35

Solve for t:

Question 36

Let And . What is
?

A)
B)
C)
D)

Question 37

Find

.

Question 38

Find

.

Question 39

An earthquake measured 5.1 on the Richter scale. How many times more powerful were the seismic waves than standard seismic waves?

Question 40

Suppose earthquake A measured 3.2 on the Richter scale. What was the Richter scale measure of earthquake B if it was 1900 times more powerful than earthquake A? Round your answer to 2 decimal places.

Question 41

What is the domain of
?

Question 42

Find the domain and asymptotes of the function

Question 43

Find the domain of the function

.

Question 44

The hydrogen ion concentration [H⁺] for a certain substance is 0.000316. What is the pH of the substance?

Question 45

If the equation is converted to the form , then a = _____ and k = _____. Give k to 4 decimal places.

Question 46

Let , with t measured in years. What is the continuous percent decay rate per year?

Question 47

Let , with t measured in years. What is the percent annual growth rate? Round to 2 decimal places.

Question 48

The doubling time for a bank account that is growing by 3.1% per year (compounded continually) is _____ years. Round 1 decimal place.

Question 49

If is converted to the form , then b = _____. Round to 3 decimal places.

Question 50

What is the half-life of a substance that decays at a rate of 3.27% per week? Round your answer to the nearest hundredth of a week.

Question 51

What annual interest rate, compounded monthly, is equivalent to an annual interest rate of 5.9% compounded continuously? Round your answer to the nearest thousandth of a percent, if necessary.

Question 52

You invest $5000 in an account earning 5% annual interest. At the same time, you invest $ in a different account earning % annual interest. In both accounts, the interest is compounded continuously. When do the accounts each hold the same amount? Round your answer to the nearest year.

Question 53

A small country is experiencing hyperinflation of 59% per month.

A) By what percent have prices climbed after 5 months?
B) If an item currently costs $12, how much will it cost after 1 year of such inflation?

Question 54

Suppose the population of an endangered species is cut in half every 55 years. Assume exponential decay.

A) What is the annual growth rate?
B) What is the continuous growth rate?
Give your answers correct to 4 decimal places.

Question 55

If 14% of a radioactive substance decays in 7 hours, what is the half-life of the substance? Round your answer to 3 decimal places.

Question 56

If 11% of a radioactive substance decays in 7 hours, what percent of the substance is left after 10 hours? Round your answer to 3 decimal places, if necessary.

Question 57

The half-life of a substance is 36 hours. If there are initially 100 grams of the substance, write a formula to determine the amount Q remaining after t hours.

Question 58

The half-life of a substance is 39 hours. If there are initially 110 grams of the substance, how many grams are remaining after 48 hours? Round your answer to 3 decimal places.

Question 59

A town with an initial population of 11,000 people doubles every 40 years. Write an equation to determine the town's population P after t years.

Question 60

A town with an initial population of 13,000 people doubles every 41 years. Determine the town's population after 9 years.

Question 61

What annual interest rate, compounded weekly, is equivalent to an annual interest rate of 5.4% compounded continuously? Round your answer to the nearest thousandth of a percent, if necessary.

Question 62

A certain country is experiencing deflation and prices are falling by 2.8% each month. If a certain item currently costs $38, how much will the item cost in a year?

Question 63

Suppose a certain population decreases by one third every 7 years. If the population is initially 19,000, what is the size of the population after 10 years? Round your answer to the nearest whole number.

Question 64

Let Which of the following is a simplified formula for ?

A)
B)
C)
D)

Question 65

The notation means that the log base is unspecified. Given that , , and , use properties of logs to find
.

Question 66

Solve t for t to 2 decimal places if possible. If not possible, enter "not possible".

Question 67

Evaluate without a calculator. Leave fractions in the form "A/B" (do not convert to decimals).

Question 68

Evaluate without a calculator.

Question 69

Rewriting the statement using exponents gives

A)
B)
C)
D)

Question 70

Rewriting the statement log y = x using exponents gives

A) 10 ^y = x
B) 10 ^x = y
C) 10 ^y = 1/x
D) 10 ^x = 1/y

Question 71

Rewriting using logs gives

A)
B)
C)
D)

Question 72

Rewriting using logs gives

A)
B)
C)
D)

Question 73

Solve using logs. Give your answer to 3 decimal places.

Question 74

Solve using logs. Give your answer to 3 decimal places.

Question 75

Does ?

Question 76

Does ?

Question 77

Let and
. What is ?

A)
B)
C)
D)

Question 78

Let . What is ?

A)
B)
C)
D)

Question 79

Let What is ?

A)
B)
C)
D)