Deck 2: Nonlinear Functions and Models

Question 1

Suppose the amount of carbon dioxide (in pounds per 15,000 miles)released by a typical sport utility vehicle (SUV)depends on its fuel efficiency according to the formula where x is a fuel efficiency of an SUV in miles per gallon. According to the model, what is the fuel efficiency of an SUV that has the least carbon dioxide pollution?

A)10 miles per gallon
B)24 miles per gallon
C)6 miles per gallon
D)11 miles per gallon
E)21 miles per gallon

Answer 1

21 miles per gallon

Question 2

Choose the logistic function that best approximates the curve.

A)
B)
C)
__________

Answer 2

Question 3

Encouraged by the popularity of your Dungeons and Dragons website, www.mudbeast.net, you have decided to charge users who log on to the site. When you charged a $1.50 access fee, your web counter showed a demand of 160 "hits" per month. After you lowered the price to $1.00, activity increased to 410 hits per month. Obtain the monthly revenue R as a function of the access fee x .

A)
B)
C)
D)
E)

Answer 3

Question 4

For the following demand equation, find the largest possible revenue.

A)500
B)250,000
C)375,000
D)125,000
E)250

Question 5

Choose the logistic function that best approximates the curve.

A)
B)
C)
__________

Question 6

The Better Baby Buggy Co. has just come out with a new model, the Turbo. The market research department predicts that the demand equation for Turbos is given by where q is the number of buggies it can sell in one month if the price is $ x per buggy. At what price should it sell the buggies to get the largest revenue? Round the result to the nearest dollar.

A)
B)
C)
D)
E)

Question 8

For the following demand equation, express the total revenue R as a function of the price p per item.

A)
B)
C)
D)
E)

Question 9

Pack-Em-In Real Estate is building a new housing development. The more houses it builds, the less people will be willing to pay, due to the crowding and smaller lot sizes. In fact, if the company builds 50 houses in this particular development, it can sell them for $200,000 each, but if it builds 70 houses, it will be able to get only $180,000 each. What is the largest possible revenue the company can get? $ __________

Question 10

The market research department of the Better Baby Buggy Co. predicts that the demand equation for its buggies is given by where q is the number of buggies it can sell in a month if the price is $ x per buggy. What is the largest monthly revenue?

A)
B)
C)
D)
E)

Question 11

For the following demand equation, find the largest possible revenue. $ __________

Question 12

The following chart shows the value of trade between two countries for the period 1994-2004 ( represents 1994). Which of the following models best approximates the data given? (Try to answer this without actually computing values.)

A)
B)
C)
D)
E)

Question 13

For the following demand equation, find the largest possible revenue.

A)
B)
C)
D)
E)

Question 14

You are the sales manager for Montevideo Productions, Inc., and you are planning to review the prices you charge clients for television advertisement development. You currently charge each client an hourly development fee of $2,000. With this pricing structure, the demand, measured by the number of contracts Montevideo signs per month, is 25 contracts. This is down 10 contracts from the figure last year, when your company charged only $1,000. Construct a linear demand equation giving the number of contracts q as a function of the hourly fee p Montevideo Productions, Inc., charges for development.

A)
B)
C)
D)
E)

Question 15

The fuel efficiency (in miles per gallon)of a sport utility vehicle (SUV)depends on its weight according to the formula where x is the weight of an SUV in pounds. According to the model, what is the weight of the least fuel-efficient SUV?

A)6,000 pounds
B)3,000 pounds
C)3,100 pounds
D)2,000 pounds
E)326 pounds

Question 16

Find the y -intercept(s)of the graph of the quadratic function.

A)
B)
C)
D) ,
E) ,

Question 17

The two fraternities Sigma Alpha Mu and Ep Sig plan to raise money jointly to benefit homeless people on Long Island. They will sell Starship Troopers T-shirts in the Student Center, but they are not sure how much to charge. Sigma Alpha Mu treasurer Solo recalls that they once sold 200 shirts in a week at $8 each, but Ep Sig treasurer Justino claims that, based on past experience, they can sell 500 per week if they charge $4 each. The university administration charges the fraternities $300 per week for use of the Student Center. What is the largest possible weekly profit, rounded to the nearest dollar?

A)$1,833
B)$533
C)$2,133
D)$800
E)$4,267

Question 18

Pack-Em-In Real Estate is building a new housing development. The more houses it builds, the less people will be willing to pay, due to the crowding and smaller lot sizes. In fact, if the company builds 60 houses in this particular development, it can sell them for $180,000 each, but if it builds 70 houses, it will be able to get only $170,000 each. What is the largest possible revenue the company can get?

A)
B)
C)
D)
E)

Question 19

You have just opened a new nightclub, Russ's Techno Pitstop, but you are unsure how much to charge for the cover charge (entrance fee). One week you charged $7 cover per guest and averaged 339 guests per night. The next week you charged $16 per guest and averaged 222 guests per night. Find the linear demand equation showing the number of guests q per night as a function of the cover charge p .

A)
B)
C)
D)
E)

Question 20

Find the vertex of the graph of the quadratic function.

A)
B)
C)
D)
E)

Question 21

The given table corresponds to the function .

Question 22

Model the data using an exponential function .

Question 23

Model the data using an exponential function . Select the correct answer.

A)
B)
C)
D)
E)

Question 24

Find an equation for exponential function that passes through the pair of points and . ( )

A)
B)
C)
D)
E)

Question 25

Which of the following three functions will be largest for large values of x ? Select the correct answer.

A)
B)
C)
D)
E)

Question 26

The given table corresponds to the function .

Question 27

The given table corresponds to the function .

Question 28

Model the data using an exponential function .

Question 29

Given the graph of the functions and . Identify which graph corresponds to . Select the correct answer.

A)Red
B)Blue

Question 30

Soon after taking an aspirin, a patient has absorbed 330 mg of the drug. If the amount of aspirin in the bloodstream decays exponentially with half being removed every 3 hours, find the amount of aspirin in the bloodstream after 7 hours. Select the correct answer.

A)654.8
B)6548
C)128.13
D)25.42
E)65.48

Question 31

Find the equation for the exponential function that passes through the pair of points and . ( )A = __________ b = __________

Question 32

Which of the following three functions will be smallest for large values of x ? Select the correct answer.

A)
B)
C)
D)
E)

Question 33

Graph the function. Select the correct answer.

A)
B)
C)
D)

Question 34

Given the graph of the functions and . Determine the color of the graph that corresponds to . Select the correct answer.

A)Blue
B)Red

Question 35

Model the data using an exponential function .

Question 36

Rock Solid Bank & Trust is offering a CD that pays 5% compounded continuously. How much interest would a $5,000 deposit earn over 15 years? (Round your answer to the nearest dollar.)Select the correct answer.

A)$5,585
B)$15,585
C)$10,395
D)$10,569
E)$10,585

Question 37

Model the data using an exponential function . Select the correct answer.

A)
B)
C)
D)
E)

Question 38

Model the data using an exponential function . Select the correct answer.

A)
B)
C)
D)
E)

Question 39

The U.S. population was 180 million in 1960 and 240 million in 1990. Assuming exponential population growth, what will the population be in the year 2020? Round your answer to the nearest million. __________ million

Question 40

The U.S. population was 180 million in 1965 and 240 million in 1995. Assuming exponential population growth, what will the population be in the year 2010? Select the correct answer.

A)270 million
B)539 million
C)250 million
D)277 million
E)1,078 million

Question 41

Soon after taking an aspirin, a patient has absorbed 350 mg of the drug. If the amount of aspirin in the bloodstream decays exponentially, with half being removed every 2 hours, find the time it will take for the amount of aspirin in the bloodstream to decrease to 290 mg. Select the answer rounded to three decimal places.

A)1.843 hours
B)5.529 hours
C)0.921 hours
D)4.607 hours
E)3.686 hours

Question 42

Plutonium-239 is used as a fuel for some nuclear reactors and also as the fissionable material in atomic bombs. It has a half-life of 24,400 years. How long will it take 14 grams of plutonium-239 to decay to 1 grams? Select the correct answer rounded to the nearest integer.

A)23,250 years
B)93,000 years
C)92,900 years
D)185,800 years
E)46,500 years

Question 43

The given table corresponds to the function .

Question 44

Use logarithms to solve the equation. (Round answers to four decimal places.)

A)
B)
C)
D)
E)

Question 45

Use logarithms to solve the equation. (Round answers to four decimal places.) x = __________

Question 46

Graph the function.

A)
B)
C)
D)
E)

Question 47

How long will it take an investment to triple if it is continuously compounded at 15% per year? Select the correct answer rounded to the nearest year.

A)4 years
B)13 years
C)7 years
D)15 years
E)8 years

Question 48

The given table corresponds to the function .

Question 49

You are trying to determine the half-life of a new radioactive element you have isolated. You start with 3 grams, and 4 days later you determine that it has decayed down to 0.1 gram. What is the half-life? Round your answer to three decimal places. Select the answer rounded to three decimal places.

A)0.815 days
B)1.630 days
C)0.408 days
D)2.446 days
E)1.223 days

Question 50

Graph the function.

A)
B)
C)
D)
E)

Question 51

How long, to the nearest year, will it take an investment in Japan to double its value if the interest is compounded every six months? Please round the answer to the nearest year. Country U.S. Japan Canada Korea Australia Yield 5.3% 1.5% 5.2% 5.4% 6.0%

A)47 years
B)46 years
C)42 years
D)51 years
E)43 years

Question 52

The table lists interest rates on long-term investments (based on 10-year government bonds)in several countries in 2004-2005. Assuming that you invest $11,000 in Japan, how long (to the nearest year)must you wait before your investment is worth $17,000 if the interest is compounded annually? Country U.S. Japan Canada Yield 5.3% 1.5% 5.2%

A)29 years
B)24 years
C)25 years
D)32 years
E)30 years

Question 53

Find the associated exponential decay model. when ; Half-life

A)
B)
C)
D)
E)

Question 54

Find the associated doubling time.

A)
B)
C)
D)
E)

Question 55

How long, to the nearest year, will it take an investment to triple if it is continuously compounded at 20% per year? Round the answers to the nearest year. __________ years

Question 56

The given table corresponds to the function .

Question 57

Convert the exponential function to the form indicated. Round all coefficients to four significant digits.

A)
B)
C)
D)
E)

Question 58

The amount of carbon-14 remaining in a sample that weighs A is given by where t is time in years. If tests on a fossilized skull reveal that 99.97% of the carbon-14 has decayed, how old is the skull? Select the correct answer rounded to the nearest integer.

A)2,629 years old
B)23,234 years old
C)0 years old
D)1,985 years old
E)28,978 years old

Question 59

Convert the exponential function to the form indicated. Round all coefficients to four significant digits.

A)
B)
C)
D)
E)

Question 60

Use logarithms to solve the equation. (Round answers to four decimal places.)

A)
B)
C)
D)
E)

Question 61

The table lists interest rates on long-term investments (based on 10-year government bonds)in several countries in 2004-2005. Assuming that you invest $13,000 in Japan, how long (to the nearest year)must you wait before your investment is worth $19,000 if the interest is compounded annually? Country U.S. Japan Canada Yield 5.3% 1.5% 5.2% __________ year(s)

Question 62

The table is filled correctly. Exponential form Logarithmic form

Question 63

Plutonium-239 is used as a fuel for some nuclear reactors and also as the fissionable material in atomic bombs. It has a half-life of 24400 years. How long will it take 20 grams of plutonium-239 to decay to 3 grams? Round your answer to the nearest year. __________ years

Question 64

Find the logistic function with the given properties. , has limiting value , and for small values of , is approximately exponential and doubles with every increase of 1 in .

A)
B)
C)
D)
E)

Question 65

Find the associated exponential decay model. when ; Half-life =

Question 66

Choose the logistic function that best approximates the curve.

A)
B)
C)
D)
E)

Question 67

Find the logistic function with the given properties. has limiting value 8 and passes through (0, 2)and (1, 6).

A)
B)
C)
D)
E)

Question 68

Find N , A , and b for the function given.

A)
B)
C)
D)
E)

Question 69

Find N , A , and b for the function.

A)
B)
C)
D)
E)

Question 70

The chart shows the number of research articles in the prominent journal Physics Review that were written by researchers in Europe during 1983-2003 ( represents 1983). Which of the following logistic functions best models the data? ( is the number of years since 1983.)Try to determine the correct model without actually computing data points.

A)
B)
C)
D)
E)

Question 71

The table below is filled correctly. Exponential form Logarithmic form

Question 72

Choose the logistic function that best approximates the given curve.

A)
B)
C)
D)
E)

Question 73

How long, to the nearest year, will it take an investment in Canada to double its value if the interest is compounded every six months? Please round the answer to the nearest year. Country U.S. Japan Canada Korea Australia Yield 5.3% 1.5% 5.2% 5.4% 6.0% t = __________ year(s)

Question 74

The table below is filled correctly. Exponential form Logarithmic form

Question 75

The following graph shows the actual percentage of U.S. households with a computer as a function of household income (the data points)and a logistic model of these data (the curve). The logistic model is where is the household income in thousands of dollars. For low incomes, the logistic model is approximately exponential. Which exponential model best approximates for small ? Round the coefficients to the nearest hundredth.

A)
B)
C)
D)
E)

Question 76

Find the logistic function with the given properties. has limiting value 16 and passes through (0, 8)and (1, 14).

A)
B)
C)
D)
E)

Question 77

The graph shows the actual percentage of U.S. households with a computer as a function of household income (the data points)and a logistic model of these data (the curve). The logistic model is where is the household income in thousands of dollars. According to the model, what percentage of extremely wealthy households had computers?

A) is close to .
B) is close to .
C) is close to .
D) is close to .
E) is close to .

Question 78

Choose the logistic function that best approximates the given curve.

A)
B)
C)
D)
E)

Question 79

Convert the exponential function to the form indicated. Round all coefficients to four significant digits. = __________ k = __________

Question 80

Find the logistic function with the given properties. , has limiting value , and for small values of , is approximately exponential and grows by 50% with every increase of 1 in .

A)
B)
C)
D)
E)