Question 1

The graph of a linear function is a:
A)curve.
B)jagged line.
C)straight line.
D)dotted line.

Accepted Answer

A linear function has a constant rate of change and therefore its graph is a straight line.

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

Accepted Answer

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

Accepted Answer

This is the formula for the velocity of a falling object near the surface of Earth, where the velocity increases by 32 feet per second for each second the object falls. Therefore, v = 32t.

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

Accepted Answer

We can use a linear equation to model the relationship between S and C:
S = 47.5 - 0.65C
Plugging in C = 15, we get:
S = 47.5 - 0.65(15) = 37.75
Therefore, the average speed when the curvature is 15 degrees is 37.75 mph, which corresponds to choice B.

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

Accepted Answer

The cost of purchasing CDs from the music club is a flat membership fee of $25 plus $10 for each CD purchased. Therefore, the equation for the cost in dollars (C) with n number of CDs bought would be C = 10n + 25.

Question 6

In the linear function y = mx + b, b is the:
A)growth rate.
B)slope.
C)initial value.
D)balance.

Accepted Answer

b is the y-intercept, which represents the initial value or the value of y when x = 0. The growth rate, slope, and balance are all represented by the coefficient m.

Question 7

A function is called linear if it has a(n) _____ growth rate.
A)increasing
B)decreasing
C)varied
D)constant

Accepted Answer

A linear function has a constant growth rate, meaning that its rate of increase or decrease stays the same over time.

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)

Accepted Answer

We are given that for every degree of rise in temperature (t), the speed of sound (S) increases by 1.1 feet per second. So, we can write:

S = 1052.3 + 1.1t

This equation shows the relation between S and t, where S is the speed of sound and t is the temperature in degrees Fahrenheit. Thus, option B is the correct choice.

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

Accepted Answer

The answer of The following table shows average life expectancy...

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

Accepted Answer

The answer of This table shows the total number of...

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

Accepted Answer

The slope (m) represents the rate of change of y with respect to x. Therefore, for every 1-unit increase in x, y changes by a factor of m.

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.

Accepted Answer

The cost per order is not a linear function of the number of CDs ordered because there is a discount applied for orders larger than 10 CDs, which introduces a piecewise function with different rates before and after the 10 CD threshold.

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

Accepted Answer

The answer of This table shows the total number of...

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

Accepted Answer

Regression is the statistical process of finding the relationship between variables. In this case, it refers to finding the best-fit line for a given set of data points. The best-fit line is the one that minimizes the distance between the line and the data points.

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

Accepted Answer

Since the average speed decreases by 0.65 mph for each additional degree of curvature, we need to multiply the amount of curvature (C) by -0.65 to get the decrease in speed. This means the formula expressing S as a linear function of C is of the form S = mC + b, where m is the slope (change in speed divided by change in curvature) and b is the y-intercept (the average speed on a straight road). Plugging in the given values, we get S = -0.65C + 47.5, which corresponds to option D.

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

Accepted Answer

The price decreased by $899 - $719 = $180 in six months.

To find the decrease in price over each month, divide $180 by 6:

$180 ÷ 6 = $30

Therefore, the price decreased by $30 each month.

The answer is 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

Accepted Answer

An exponential function is a function in which the independent variable is in the exponent, resulting in a constant percentage change in the output for each unit change in the input. This means that as the input increases, the output increases at an accelerating rate.

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)

Accepted Answer

The answer of A salesman earns a base salary of...

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

Accepted Answer

The speed of sound increases by 1.1 feet per second for every degree of rise in temperature. So, if the speed of sound is 1131.5 feet per second, then the temperature is (1131.5 - 1052.3) / 1.1 = 72 degrees Fahrenheit.

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

Accepted Answer

First, we need to find the number of degrees above 0 degrees Fahrenheit to calculate the increase in speed of sound.

67 degrees Fahrenheit - 0 degrees Fahrenheit = 67 degrees

Now, we can use the given formula to calculate the increase in speed of sound:

67 degrees x 1.1 feet per second per degree = 73.7 feet per second

Finally, we add this increase to the speed of sound at 0 degrees Fahrenheit:

1052.3 feet per second + 73.7 feet per second = 1126 feet per second

Therefore, the speed of sound at 67 degrees Fahrenheit is 1126 feet per second, which is answer choice D.

Quiz 3: Linear and Exponential Change: Comparing Growth Rates

The graph of a linear function is a:

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:

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:

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

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

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.

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.

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

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.

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.

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

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

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

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.

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.