Deck 11: Exponential Functions

Question 1

Let and evaluate

A)
B)
C)
D)
E)

Answer 1

B

Question 2

Suppose you deposit $1,600 in an account with an annual interest rate of 5% compounded quarterly. Find the amount of money in the account after 11 years.

A) $1,834.28
B) $13,691.44
C) $2,736.54
D) $2,480.00
E) $2,763.77

Answer 2

E

Question 3

Suppose you deposit $1,000 in an account with an annual interest rate of 9% compounded quarterly. How many years will it take for the account to contain $3,000?

A) 3.19 years
B) 12.75 years
C) 49.37 years
D) 14.87 years
E) 12.34 years

Answer 3

E

Question 4

Let Evaluate

A)
B)
C)
D)
E)

Question 5

The function where V is value and t is time in years, can be used to find the value of a printing press during the first 7 years of use. After how many years will the printing press be worth only $45,000?

A) 8 years, 2 months
B) 10 years, 5 months
C) 10 years, 9 months
D) 7 years, 10 months
E) 5 years, 11 months

Question 6

Choose the graph of the function below.

A)
B)
C)
D)

Question 7

A golf ball is manufactured so that if it is dropped from A feet above the ground onto a hard surface, the maximum height of each bounce will be of the height of the previous bounce. Find an exponential equation that gives the height h the ball will attain during the n th bounce. If the ball is dropped from 100 feet above the ground onto a hard surface, how high will it bounce on the 7th bounce?

A) The exponential equation is the height of the 7th bounce is approximately 0.051 feet.
B) The exponential equation is the height of the 7th bounce is approximately 0.292 feet.
C) The exponential equation is the height of the 7th bounce is approximately 0.046 feet.
D) The exponential equation is the height of the 7th bounce is approximately 0.034 feet.
E) The exponential equation is the height of the 7th bounce is approximately 0.031 feet.

Question 8

Let and evaluate

A)
B)
C)
D)
E)

Question 9

Automobiles built before 1993 use Freon in their air conditioners. The federal government now prohibits the manufacture of Freon. Because the supply of Freon is decreasing, the price per pound is increasing exponentially. Current estimates put the formula for the price per pound of Freon at where t is the number of years since 1990. Find the price of Freon in 1990 and 1999. What is the anticipated cost for Freon in the year 2009?

A) $1.89 in 1990, $13.74 in 1999 and $131.15 in 2009
B) $1.89 in 1990, $13.14 in 1999 and $25.64 in 2009
C) $1.89 in 1990, $14.08 in 1999 and $131.15 in 2009
D) $1.89 in 1990, $21.26 in 1999 and $44.89 in 2009
E) $1.89 in 1990, $14.08 in 1999, and $130.63 in 2009

Question 10

The function where V is value and t is time in years, can be used to find the value of a crane for the first 6 years of use. What is the value of the crane after 2 years and 4 months?

A) $152,276
B) $153,577
C) $153,510
D) $150,814
E) $150,903

Question 11

Choose the graph of the function below.

A)
B)
C)
D)

Question 12

Let Evaluate g (-2).

A)
B)
C)
D)
E)

Question 13

The function where V is value and t is time in years, can be used to find the value of a printing press during the first 7 years of use. What is the value of the printing press after 4 years and 6 months?

A) $76,816
B) $76,588
C) $76,656
D) $73,981
E) $75,354

Question 14

Choose the graph of the function below.

A)
B)
C)
D)

Question 15

A painting is purchased as an investment for $200. If the painting s value doubles every 6 years, then its value is given by the function where t is the number of years since it was purchased, and V ( t ) is its value (in dollars) at that time. How many years will it take for the painting to be worth $800?

A) 12 years
B) 17 years
C) 14 years
D) 9 years
E) 11 years

Question 16

In 1990, $699 billion were spent on health care. Health care expenditures, E , in billions of dollars, can be estimated using the function where t is time in years since 1970 (U.S. Census Bureau.) What are the expected health care expenditures in 2009, 2010, and 2011?

A) $4,445 billion in 2009, $5,080 billion in 2010 and $5,639 billion in 2011.
B) $4,577 billion in 2009, $5,225 billion in 2010 and $5,806 billion in 2011.
C) $4,445 billion in 2009, $5,080 billion in 2010 and $5,806 billion in 2011.
D) $4,577 billion in 2009, $5,080 billion in 2010 and $5,639 billion in 2011.
E) $4,445 billion in 2009, $5,225 billion in 2010 and $5,639 billion in 2011.

Question 17

The function where V is value and t is time in years, can be used to find the value of a crane for the first 6 years of use. How much time must pass before the crane will be worth only $80,000?

A) 8 years and 9 months
B) 6 years and 3 months
C) 8 years and 4 months
D) 5 years and 10 months
E) 10 years and 3 months

Question 18

Suppose you deposit $1,500 in an account with an annual interest rate of 9% compounded continuously. How much money would the account contain after 5 years.

A) $2,352.47
B) $2,478.34
C) $2,210.05
D) $2,239.33
E) $2,528.34

Question 19

The half-life of iodine-131 is 8 days. If a patient is administered a 1,700-microgram dose of iodine-131 , how much iodine-131 will be in the patient's system after 8 days and after 22 days?

A) 850 micrograms after 8 days; 265.1 micrograms after 22 days
B) 850 micrograms after 8 days; 239.6 micrograms after 22 days
C) 850 micrograms after 8 days; 252.7 micrograms after 22 days
D) 850 micrograms after 8 days; 425 micrograms after 22 days
E) 850 micrograms after 8 days; 258.5 micrograms after 22 days

Question 20

Choose the graph of the function below.

A)
B)
C)
D)

Question 21

Suppose you deposit $1,600 in an account with an annual interest rate of 9% compounded quarterly. Find the amount of money in the account after 15 years. Please round your answer to the nearest cent. $__________

Question 22

Automobiles built before 1993 use Freon in their air conditioners. The federal government now prohibits the manufacture of Freon. Because the supply of Freon is decreasing, the price per pound is increasing exponentially. Current estimates put the formula for the price per pound of Freon at where t is the number of years since 1990. Find the price of Freon in 1990. Please round your answer to the nearest cent. $__________ per pound Find the price of Freon in 1998. Please round your answer to the nearest cent. $__________ per pound How much will Freon cost in the year 2007?. Please round your answer to the nearest cent. $__________ per pound

Question 23

For the following one-to-one function, find the equation of the inverse.

A)
B)
C)
D)
E)

Question 24

The half-life of iodine-131 is 8 days. A patient is administered a 1,100-microgram dose of iodine-131 . How much iodine-131 will be in the patient's system after 8 days? __________ micrograms How much iodine-131 will be in the patient's system after 21 days? Please round your answer to one decimal place. __________ micrograms

Question 25

The function where V is value and t is time in years, can be used to find the value of a crane for the first 6 years of use. What is the value of the crane after 4 years and 3 months? Please round your answer to the nearest dollar. $ __________

Question 26

For the following one-to-one function, find the equation of the inverse.

A)
B)
C)
D)
E)

Question 27

Suppose you deposit $1,900 in an account with an annual interest rate of 7% compounded continuously. How much money would the account contain after 3 years. Please round your answer to the nearest cent. $__________

Question 28

For the following one-to-one function, find the equation of the inverse.

A)
B)
C)
D)
E)

Question 29

The function where V is value and t is time in years, can be used to find the value of a printing press during the first 7 years of use. How many years must pass before the printing press will be worth only $55,000? Please round your answer to the nearest month. __________ year(s) __________ month(s)

Question 30

For the following one-to-one function, find the equation of the inverse.

A)
B)
C)
D)
E)

Question 31

The function where V is value and t is time in years, can be used to find the value of a printing press during the first 7 years of use. What is the value of the printing press after 5 years and 4 months? Please round your answer to the nearest dollar. $__________

Question 32

Let and evaluate

Question 33

Suppose you deposit $1,100 in an account with an annual interest rate of 6% compounded quarterly. How many years will it take for the account to contain $3,300? Please round your answer to two decimal places. __________ years

Question 34

Let Evaluate . = __________

Question 35

Let Evaluate . = __________

Question 36

For the following one-to-one function, find the equation of the inverse.

A)
B)
C)
D)
E)

Question 37

In 1990, $699 billion were spent on health care. Health care expenditures, E , in billions of dollars, can be estimated using the function where t is time in years since 1970 (U.S. Census Bureau.) What is the expected health care expenditure in 2005? Round to the nearest billion. $ __________ billion What is the expected health care expenditure in 2006? Round to the nearest billion. $ __________ billion What is the expected health care expenditure in 2007? Round to the nearest billion. $ __________ billion

Question 38

Let and evaluate

Question 39

A painting is purchased as an investment for $200. If the painting s value doubles every 3 years, then its value is given by the function where t is the number of years since it was purchased, and V ( t ) is its value (in dollars) at that time. How many years must pass before the painting is worth $3,200? __________ years

Question 40

The function where V is value and t is time in years, can be used to find the value of a crane for the first 6 years of use. How much time must pass before the crane will be worth only $55,000? Please round your answer to the nearest month. __________ year(s) __________ month(s)

Question 41

Determine if the following function is one-to-one.

A) The given function is not one-to-one.
B) The given function is one-to-one.

Question 42

For the following one-to-one function, find the equation of the inverse.

Question 43

If then Use these two functions to find and

A)
B)
C)
D)
E)

Question 44

Use the functions defined in Tables 1 and 2 to answer the following questions. Table 1 Table 2 x f ( x ) x g ( x ) - 9 5 - 5 4 4 - 5 - 4 5 5 - 4 5 - 9 9 6 6 9 What are the domain and range of f ? What are the domain and range of g ? How are the domain and range of f related to the domain and range of g ?

A) -------------------------------------------------
B) -------------------------------------------------
C) -------------------------------------------------
D) -------------------------------------------------

Question 45

If find

A)
B)
C)
D)
E)

Question 46

Could the following table of values represent ordered pairs from a one-to-one function? x y - 2 0.5 - 1 0.6 0 0.7 1 0.8 2 0.9

A) The given table of values could represent ordered pairs from a one-to-one function.
B) The given table of values could not represent ordered pairs from a one-to-one function.

Question 47

Evaluate the function using the tables given below. Table 1 Table 2 x f ( x ) x g ( x ) - 8 4 - 4 1 1 - 4 - 1 4 4 - 1 4 - 8 8 5 5 8

A)
B)
C)
D)
E)

Question 48

For the following one-to-one function, find the equation of the inverse.

A)
B)
C)
D)
E)

Question 49

Evaluate the function using the tables given below. Table 1 Table 2 x f ( x ) x g ( x ) - 8 6 - 6 4 4 - 6 - 4 6 6 - 4 6 - 8 8 7 7 8

A)
B)
C)
D)
E)

Question 50

For the following one-to-one function, find the equation of the inverse.

Question 51

For , choose the graph of the relation and its inverse.

A)
B)
C)
D)
E)

Question 52

For , choose the graph of the relation and its inverse.

A)
B)
C)
D)
E)

Question 53

For the following one-to-one function, find the equation of the inverse.

Question 54

Evaluate the function using the tables given below. = __________ Table 1 Table 2 x f ( x ) x g ( x ) - 9 6 - 6 4 4 - 6 - 4 6 6 - 4 6 - 9 9 7 7 9

Question 55

If then Use these two functions to find and

A)
B)
C)
D)
E)

Question 56

For the following one-to-one function, find the equation of the inverse.

A)
B)
C)
D)
E)

Question 57

For , choose the graph of the relation and its inverse.

A)
B)
C)
D)

Question 58

Evaluate the function using the tables given below. = __________ Table 1 Table 2 x f ( x ) x g ( x ) - 8 2 - 2 1 1 - 2 - 1 2 2 - 1 2 - 8 8 6 6 8

Question 59

For , choose the graph of the relation and its inverse.

A)
B)
C)
D)
E)

Question 60

Use the functions defined in Tables 1 and 2 to answer the following questions. Table 1 Table 2 x f ( x ) x g ( x ) - 6 - 3 - 3 1 1 3 - 1 3 3 - 1 3 6 6 5 5 - 6 Is f a one-to-one function? Is g a one-to-one function?

A) f is a one-to-one function; g is a one-to-one function
B) f is a one-to-one function; g is not a one-to-one function
C) f is not a one-to-one function; g is a one-to-one function
D) f is not a one-to-one function; g is not a one-to-one function

Question 61

For the following one-to-one function, find the equation of the inverse.

Question 62

Solve the equation for x .

A)
B)
C)
D)
E)

Question 63

Choose the answer that shows the equation in exponential form.

A)
B)
C)
D)
E)

Question 64

Choose the answer that shows the equation in logarithmic form.

A)
B)
C)
D)
E)

Question 65

Choose the answer that shows the equation in logarithmic form.

A)
B)
C)
D)
E)

Question 66

If find

Question 67

Solve the equation for x .

A)
B)
C)
D)
E)

Question 68

Solve the equation for x .

A)
B)
C)
D)
E)

Question 69

For the following one-to-one function, find the equation of the inverse.

Question 70

Choose the answer that shows the equation in logarithmic form.

A)
B)
C)
D)
E)

Question 71

For the following one-to-one function, find the equation of the inverse.

Question 72

For the following one-to-one function, find the equation of the inverse.

Question 73

Choose the answer that shows the equation in exponential form.

A)
B)
C)
D)
E)

Question 74

Solve the equation for x .

A)
B)
C)
D)
E)

Question 75

Determine if the following function is one-to-one. Answer yes or no .

Question 76

Choose the answer that shows the equation in exponential form.

A)
B)
C)
D)
E)

Question 77

where is the concentration of the hydrogen ions in solution. A hair conditioner has a pH of 6. Find the concentration of hydrogen ions in the conditioner.

A)
B)
C)
D)
E)

Question 78

Choose the answer that shows the equation in exponential form.

A)
B)
C)
D)
E)

Question 79

Could the following table of values represent ordered pairs from a one-to-one function? Answer yes or no . x y - 2 0.3 - 1 0.5 0 0.7 1 0.9 2 1.1

Question 80

Use the functions defined in Tables 1 and 2 to answer the following questions. Table 1 Table 2 x f ( x ) x g ( x ) - 8 - 4 - 4 1 1 4 - 1 4 4 - 1 4 - 8 8 5 5 8 Is f a one-to-one function? __________ Is g a one-to-one function? __________