Deck 3: Linear and Exponential Change: Comparing Growth Rates

Question 1

The graph of a linear function is a:

A)curve.
B)jagged line.
C)straight line.
D)dotted line.

Answer 1

C

Question 2

Suppose you are at the base of a hill, and you see a sign that reads "Elevation 4000 feet." The road you are on goes straight up the hill to the top, where you see another sign that reads "Elevation 4500 feet." If the top of the hill is 5 horizontal miles from the base, what is the growth rate in your elevation with respect to horizontal distance as you drive up the road?

A)150 feet per mile
B)100 feet per mile
C)200 feet per mile
D)500 feet per mile

Answer 2

B

Question 3

If we drop a rock near the surface of Earth, its velocity increases by 32 feet per second for each second the rock falls. If v is the velocity in feet per second and t is the time in seconds:

A)v = 32t
B)t = 32v
C)v = t + 32
D)t = v + 32

Answer 3

A

Question 4

On rural highways, the average speed S (in miles per hour) is related to the amount of curvature C (in degrees) of the road. Suppose that on a straight road (C = 0), the average speed is 47.5 miles per hour and that this decreases by 0.65 mph for each additional degree of curvature. What is the average speed if the curvature is 15 degrees?

A)42.35 mph
B)37.75 mph
C)57.15 mph
D)38.35 mph

Question 5

Suppose that the cost of purchasing CDs from a music club is a flat membership fee of $25 plus $10 for each CD purchased. If C is the cost in dollars and n is the number of CDs bought, then the amount of money you pay would be:

A)C = 25n + 10
B)C = 10n + 25
C)C = 25n - 10
D)C = 10 - 25n

Question 6

In the linear function y = mx + b, b is the:

A)growth rate.
B)slope.
C)initial value.
D)balance.

Question 7

A function is called linear if it has a(n) _____ growth rate.

A)increasing
B)decreasing
C)varied
D)constant

Question 8

The speed of sound at 0 degrees Fahrenheit is 1052.3 feet per second. For every degree of rise in temperature (t), the speed of sound (S) increases by 1.1 feet per second. Find the relation between the S and t.

A)
B)
C)
D)

Question 9

The following table shows average life expectancy in years at birth in the given year:
If t denotes the time in years since 2003 and E is the life expectancy in years, then the trend line for this data is given by E = 0.18t + 77.16. If this trend line persisted through 2012, what would be the average life expectancy in years of a child born in 2012?

A)78.8 years
B)79.0 years
C)78.6 years
D)79.2 years

Question 10

This table shows the total number of patients diagnosed with the flu since an outbreak started: Find the slope of the linear function giving the number of diagnosed flu cases per day.

A)0.7
B)0.9
C)1.2
D)1.4

Question 11

For the linear function y = mx + b, each 1-unit increase in x corresponds to a change of _____ unit(s) in y.

A)1
B)2
C)m
D)b

Question 12

Suppose that a music club charges $12 per CD but offers a 5% discount on orders larger than 10 CDs. The cost per order is a linear function of the number of CDs ordered.

Question 13

This table shows the total number of patients diagnosed with the flu since an outbreak started: Find the formula for the linear function giving the number of diagnosed flu cases in terms of time if F is the number of flu patients diagnosed and d is time in days.

A)F = 21d + 0.7
B)F = 0.7d + 21
C)F = 1.4d + 21
D)F = 2.1d + 0.7

Question 14

Given a set of data points, the _____ line comes as close as possible to fitting those data.

A)interpretation
B)regression
C)stabilizing
D)growth

Question 15

On rural highways, the average speed S (in miles per hour) is related to the amount of curvature C (in degrees) of the road. Suppose that on a straight road (C = 0), the average speed is 47.5 miles per hour and this decreases by 0.65 mph for each additional degree of curvature. Find the formula expressing S as a linear function of C.

A)S = 0.65C + 47.5
B)S = 47.5C + 0.65
C)S = 47.5C - 0.65
D)S = -0.65C + 47.5

Question 16

A new laptop computer selling for $899 in January fell in price to $719 in six months. Assuming the relationship of price to time is linear, determine the decrease in price over each month.

A)$45
B)$40
C)$35
D)$30

Question 17

A(n) _____ function is a function that changes at a constant percentage rate.

A)logarithmic
B)linear
C)exponential
D)increasing

Question 18

A salesman earns a base salary of $1500 a month plus 4% of his monthly sales. In that case:

A)
B)
C)
D)

Question 19

The speed of sound at 0 degrees Fahrenheit is 1052.3 feet per second. For every degree of rise in temperature, the speed of sound increases by 1.1 feet per second. If the speed of sound is 1131.5 feet per second, then the temperature is _____ degrees Fahrenheit.

A)72
B)77
C)82
D)87

Question 20

The speed of sound at 0 degrees Fahrenheit is 1052.3 feet per second. For every degree of rise in temperature, the speed of sound increases by 1.1 feet per second. At 67 degrees the speed of sound is _____ feet per second.

A)73.7
B)1119.3
C)1053.4
D)1126.0

Question 21

If the decibel of a sound is doubled, then the relative intensity will be:

A)doubled.
B)squared.
C)increased by a factor of 10.
D)increased by a factor of 100.

Question 22

Suppose the number of Internet domain hosts grew according to the rule Next year's number = 1.47 × Current number. If the number of domain hosts initially was 8.4 million, find an exponential function that gives the number of hosts, H, in terms of time, t

A)H = 1.47 × (8.4)^t
B)H = 1.47 + (8.4)^t
C)H = 8.4 + (1.47)^t
D)H = 8.4 × (1.47)^t

Question 23

The _____ of a radioactive substance is the time it takes for half of the substance to decay.

A)doubling time
B)half-life
C)shelf-life
D)halving time

Question 24

The formula for an exponential function y of t is:

A)y = Initial value × Base
B)y = Initial value × (Base)^t
C)y = Base × (Initial value)^t
D)y = Initial value + (Base)^t

Question 25

An ordinary sheet of paper is about a tenth of a millimeter thick. Find an exponential formula that gives the thickness, T, in millimeters after n folds.

A)T = 0.1 × 2ⁿ
B)T = 0.1 × 4ⁿ
C)T = 0.2 × (0.5)ⁿ
D)T = 0.1 × (0.5)ⁿ

Question 26

Actinium-225 has a half-life of 10 days. Suppose we have an initial amount of 100 grams of actinium-225. How much would be present after 30 days?

A)50 grams
B)33.3 grams
C)25 grams
D)12.5 grams

Question 27

If a population grows exponentially as time increases, then time _____ as population increases.

A)grows exponentially
B)grows logarithmically
C)decays exponentially
D)decays logarithmically

Question 28

From 1929 to the early 1930s, the prices of consumer goods actually decreased. Economists call this phenomenon deflation. The rate of deflation during this period was around 7% per year. Suppose this rate of deflation persisted over 20 years. What would be the cost after 20 years of an item that cost $500 initially?

A)$23.25
B)$61.66
C)$271.90
D)$117.12

Question 29

The _____ of an earthquake is the logarithm of relative intensity.

A)magnitude
B)scale
C)Richter value
D)degree

Question 30

Suppose that in January there is a magnitude 4.5 earthquake hitting the East Coast of the United States. Six months later, a magnitude 6.5 earthquake hits the West Coast. How many times more intense was the West Coast quake than the East Coast quake?

A)2
B)10
C)100
D)1000

Question 31

The probability P (as a decimal) that no tsunami with waves over 15 feet high will strike a beach community over a period of t years is given by the formula P = 0.93^t. What is the percentage decrease of the probability for each 1-year increase in the time interval?

A)3%
B)5%
C)7%
D)9%

Question 32

The following table shows the number of certain objects for given time . Which of the following best describes as a function of ?

A)linear
B)exponential
C)logarithmic
D)constant

Question 33

The probability P (as a decimal) that a tsunami with waves over 15 feet high will NOT strike a beach community over a period of t years is given by the formula P = 0.93^t. What is the probability that someone living in the beach community for 20 years will NOT encounter a tsunami with waves 15 feet or higher?

A)23.4%
B)18.6%
C)33.7%
D)14.0%

Question 34

An investment grows according to the rule: Next month's balance = 1.003 × Current balance. Find the percentage increase for one year.

A)0.003%
B)1.81%
C)0.3%
D)12.036%

Question 35

The rate of inflation measures the percentage increase in the price of consumer goods. The rate of inflation from the year 2005 to 2007 was 5%. Suppose that this rate persisted through 2015. What would be the cost in 2015 of an item that costs $100 in 2005?

A)$127.63
B)$135.89
C)$149.63
D)$162.89

Question 36

The number of blogs (or weblogs) grew rapidly for several years. According to one report, since early 2004 the number of blogs has doubled in size every six months. What is the percent increase from March 2004 to March 2006?

A)1500%
B)1600%
C)3100%
D)3200%

Question 37

Initially, a population is 750, and it grows by 3% each year. Find a formula for the population, P, at any time, t.

A)P = 1.03 × (750)^t
B)P = 0.03 × (750)^t
C)P = 750 × (1.03)^t
D)P = 750 × (0.03)^t

Question 38

Suppose Mark's salary grows by $2500 each year and Sarah's salary grows by 2.5% each year. Which one has a salary that grows exponentially?

A)Mark
B)Sarah
C)Both
D)Neither

Question 39

An exponential function y of t is characterized by the following property: When t increases by 1, to find the new value of y, we multiply the current value by _____.

A)t + 1
B)t - 1
C)the initial value
D)the base

Question 40

For traffic that flows on a highway, the headway is the average time between vehicles. On four-lane highways, the probability P (as a decimal) that the headway is at least t seconds when there are 500 vehicles per hour traveling one way is given by P = 0.87^t. Under these circumstances, what is the probability that the headway is at least 15 seconds?

A)13.05%
B)12.38%
C)11.45%
D)10.55%

Question 41

The acidity of a solution is determined by the concentration H of hydrogen ions. The formula is . The accompanying exponential formula is H = 0.1^pH. Lower pH values indicate a more acidic solution. Normal rain has a pH of 5.6. Suppose acid rain has a pH of 4.3. How many times as acidic as normal rain is this?

A)2
B)5
C)10
D)20

Question 42

In an area prone to earthquakes there is a 6.9 magnitude quake. Two years before there was a 6.6 magnitude quake. The relative intensity of the 6.9 quake was about twice that of the 6.6 quake.

Question 43

Solve the equation .

A)
B)
C)
D)

Question 44

Which of the following is a quadratic function?

A)
B)
C)
D)

Question 45

Which of the following statements is NOT correct for the function ?

A)The function is a quadratic function.
B)The graph of is open downward.
C)The vertex of the graph of is .
D)The function has 2 distinct real zeros.

Question 46

How many times more intense is a 6.0 magnitude earthquake than a 3.0 magnitude earthquake?

A)2
B)3
C)100
D)1000

Question 47

The graph of a quadratic function has a special shape known as a:

A)line.
B)parabola.
C)hyperbola.
D)ellipse.

Question 48

Suppose that inflation is 3% per year. This means the cost of an item increases by 3% each year. Suppose a jacket cost $150 in 2011. How long will it take for the jacket to cost $200 dollars?

A)5 years
B)10 years
C)15 years
D)20 years

Question 49

Radium-226 is subject to radioactive decay, and each year the amount present is reduced by 4.2%. The amount of radium-226 is an exponential function of time in years. What is the base of this exponential function?

A)0.042
B)0.238
C)0.958
D)4.2

Question 50

What is the number of distinct real solutions for the equation ?

A)0
B)1
C)2
D)3

Question 51

Suppose you make an investment of $2000 that you are not allowed to cash in for five years. Unfortunately, the value of the investment decreases by 15% per year. How long will it be before your investment decreases to half its original value?

A)2.5 years
B)3.6 years
C)4.1 years
D)4.3 years

Question 52

A speaker is playing music at 75 decibels. A second speaker playing the same music at the same decibel reading is placed beside the first. What is the decibel reading of the pair of speakers?

A)150 decibels
B)180 decibels
C)98 decibels
D)78 decibels

Question 53

The loudness of sound decreases as the distance from the source increases. Doubling the distance from a sound multiplies the relative intensity of the sound by one-fourth. When the sound of a speaker is recorded as 80 decibels at 10 feet, what is the decibel reading if four identical speakers are added at 20 feet?

A)83 decibels
B)84 decibels
C)92 decibels
D)93 decibels

Question 54

An increase of 1 on the pH scale causes acidity to be multiplied by a factor of 0.1, while a decrease of 1 on the pH scale causes acidity to be multiplied by a factor of 10. If pure water has a pH of 7, how many times as acidic as pure water is a solution measuring a pH of 3?

A)10
B)100
C)1000
D)10,000

Question 55

The loudness of sound decreases as the distance from the source increases. Doubling the distance from a sound multiplies the relative intensity of the sound by one-fourth. If the sound of a speaker is recorded at 80 decibels at 4 feet, what is the decibel reading at 8 feet?

A)20 decibels
B)46 decibels
C)68 decibels
D)74 decibels

Question 56

An investment is growing by 9% each year. How long does it take the investment to double in value?

A)7 years
B)8 years
C)10 years
D)11 years

Question 57

Suppose that inflation is 3% per year. This means the cost of an item increases by 3% each year. Suppose a jacket cost $150 in 2011. Find a formula that gives the cost of the jacket C in dollars after t years.

A)C = $150 + 1.03^t
B)C = $150 × 1.03^t
C)C = $150 × 1.3^t
D)C = $150 + 1.3^t

Question 58

Factor the equation .

A)
B)
C)
D)

Question 59

If the per capita growth rate of the world population continues to be what it was in the year 2000, the world population t years after July 1, 2000, will be 6.085 × 1.0121^t billion. According to this formula, when will the world population reach 9 billion?

A)41.3 years after July 1, 2000
B)32.5 years after July 1, 2000
C)22.7 years after July 1, 2000
D)6.8 years after July 1, 2000

Question 60

What is the product of two solutions of the equation ?

A)-10
B)24
C)-24
D)10

Question 61

A small business has the following revenue and cost functions for a product: and . If the break-even point lies where revenue equals cost, how many break-even points are there?

A)0
B)1
C)2
D)3

Question 62

A ball is hit upward with an initial velocity of 128 feet per second. After seconds, its height is given by the function . How many seconds does the ball take to reach its maximum height?

A)4.0 seconds
B)4.5 seconds
C)5.0 seconds
D)5.5 seconds

Question 63

A ball is hit upward with an initial velocity of 128 feet per second. After seconds, its height is given by the function . What is the maximum height in feet of the ball?

A)256 feet
B)260 feet
C)264 feet
D)268 feet

Question 64

What value of makes a minimum?

A)1.5
B)2
C)3
D)3.5

Question 65

Suppose that a rifle bullet follows a parabolic path given by , where both and are measured in feet. How far downrange will the bullet hit the ground?

A)2000 feet
B)2200 feet
C)2500 feet
D)3000 feet

Question 66

What is the maximum value of the function ?

A)200
B)230
C)250
D)280

Question 67

Cutting 7-inch-long squares from a square piece of cardboard and folding up the edges, you want to make an open box (without lid) with a square bottom, a height of 7 inches, and a volume of 252 cubic inches. What should be the dimension of the cardboard?

A)
B)
C)
D)

Question 68

A walkway of a park has the shape of a right triangle with three side lengths . Find the perimeter of the right triangle.

A)240
B)270
C)285
D)300

Question 69

You have a 400-foot roll of fencing to enclose a playground. If you want to construct a rectangular playground, what is the largest possible area of the playground?

A)
B)
C)
D)

Question 70

You have a 600-foot roll of fencing to enclose two separate rectangular playgrounds for different age groups. If the two playgrounds are identical and adjacent, and form a larger rectangular region, what is the largest possible area of the playgrounds in total?

A)
B)
C)
D)

Question 71

A rectangular playground has the dimensions 20 yards by 30 yards. You want to double the space by adding the same amount to both the length and width. What is the perimeter of the expanded playground?

A)140 yards
B)160 yards
C)180 yards
D)120 yards

Question 72

For a certain product X, the profit is modeled as , where equals the number of units sold. How many units sold will produce the maximum profit?

A)20 units
B)50 units
C)100 units
D)200 units