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| Section | Objectives |
|---|---|
| Topic 1: Functions and Graphs | - Function Concepts
|
| Topic 2: Linear Functions and Systems | - Linear Equations
|
| Topic 3: Polynomial and Rational Expressions | - Rational Expressions
|
| Topic 4: Exponential and Logarithmic Concepts | - Logarithmic Basics
|
| Topic 5: Foundations of Algebra | - Algebraic Expressions
|
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NEW QUESTION # 45
The graph shows the estimated wait time, in minutes, based on the number of hours after 7:00 a.m.
What is the average rate of change of the wait time from point Ato point B?
Answer: A
Explanation:
From the graph, the horizontal axis represents:
t= " hours after 7:00 a.m. "
The vertical axis represents:
" estimated wait time in minutes "
Point Ais approximately at:
A=(5,88.3)
Point Bis approximately at:
B=(9,65)
The average rate of change from point Ato point Bis calculated using:
(y_2-y_1)/(x_2-x_1 )
Substitute the values:
(65-88.3)/(9-5)
=(-23.3)/4
=-5.825
Rounded to two decimal places:
-5.83
So, the wait time decreases by about:
5.83 " minutes per hour "
NEW QUESTION # 46
The populations, in thousands, of two towns are shown in the graph, where the horizontal axis measures the time in years.
Which town's population is growing at a faster rate?
Answer: D
Explanation:
The graph compares the populations of two towns over time.
The horizontal axis represents:
" Time in years "
The vertical axis represents:
" Population in thousands "
The graph shows:
Town A as the solid blue line.
Town B as the dashed blue line.
To determine which town's population is growing faster, we compare the slopes of the two lines.
In Applied Algebra, the slope of a line represents the rate of change:
" slope " = " change in population " / " change in time "
From the graph:
" Town A grows at about " 0.9 " thousand people per year "
" Town B grows at about " 1.6 " thousand people per year "
Now compare the growth rates:
1.6 > 0.9
So Town B's population is growing at a faster rate.
The values 8.0and 6.5describe starting populations, not growth rates. Since the question asks about growing at a faster rate, we must compare the slopes.
NEW QUESTION # 47
The number of people auditioning for a game show is expected to be 4 times the number of people who auditioned last year. The function A(t) can be used to model the situation, where t represents the number of people who auditioned last year and A represents the number of people expected to audition this year.
Which quantity represents the number of people expected to audition this year, given that 330 people auditioned last year?
Answer: C
Explanation:
We are told that the number of people expected to audition this year is 4 times the number of people who auditioned last year.
Let:
t=number of people who auditioned last year
and
A(t)=number of people expected to audition this year
Since this year's number is 4 times last year's number, the function is:
A(t)=4t
The question says that 330 people auditioned last year, so:
t=330
Now substitute 330 into the function:
A(330)=4(330)
A(330)=1320
So, the correct function notation is:
A(330)=1,320
This means: when 330 people auditioned last year, 1,320 people are expected to audition this year.
Therefore, the correct answer is:
B
NEW QUESTION # 48
The function P(t)represents the daily profit, in hundreds of dollars, for a museum since opening. The graph of P(t)is shown.
What is the correct interpretation of the maximum value?
Answer: B
Explanation:
The graph shows a curved, downward-opening function. This type of graph is commonly associated with a quadratic polynomial function.
The maximum value of a downward-opening parabola occurs at its highest point, called the vertex.
From the graph, the highest point occurs at approximately:
t=9.5
This means the museum reaches its maximum daily profit approximately:
9.5 " years after opening "
The vertical axis represents daily profit in hundreds of dollars. From the graph, the maximum P(t)-value is approximately:
16.5
Since the profit is measured in hundreds of dollars:
16.5×100=1650
So the maximum daily profit is approximately:
$1,650
Therefore, the correct interpretation is:
" Approximately 9.5 years after opening, a maximum daily profit of approximately " $1,650 " was earned. "
NEW QUESTION # 49
The spread of two viruses within a single population is modeled using the functions in the graph.
What is a correct conclusion based on the graph?
Answer: D
Explanation:
The graph compares the spread of two viruses over time.
The horizontal axis represents:
t= " time in months "
The vertical axis represents:
" percentage of the population affected "
The graph shows:
Virus A as the solid blue curve.
Virus B as the dashed blue curve.
To determine which statement is correct, we compare when each virus reaches the same population percentage.
At 20%:
Virus B reaches 20%earlier, around t#5months.
Virus A reaches 20%later, around t#6.5months.
So Virus B affects 20%of the population before Virus A does.
For higher percentages such as 60%, 70%, and 80%, Virus A rises more quickly after about 50%, so Virus A reaches those percentages before Virus B.
Therefore, the correct conclusion is:
" Virus B affects " 20% " of the population before virus A does. "
NEW QUESTION # 50
......
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