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| Section | Objectives |
|---|---|
| Topic 1: Exponential and Logarithmic Concepts | - Exponential Functions
|
| Topic 2: Linear Functions and Systems | - Linear Equations
|
| Topic 3: Foundations of Algebra | - Algebraic Expressions
|
| Topic 4: Polynomial and Rational Expressions | - Rational Expressions
|
| Topic 5: Functions and Graphs | - Graphing Functions
|
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NEW QUESTION # 111
The number of letters processed daily at a mail center is modeled by the decreasing exponential function shown in the graph.
Which value is the number of letters processed per day trending toward as time progresses, based on the equation of the horizontal asymptote?
Answer: A
Explanation:
The graph shows a decreasing exponential function.
The vertical axis represents:
" Letters per day "
The horizontal axis represents:
" Time in years "
For an exponential decay graph, the value decreases quickly at first and then begins to level off. The value it approaches in the long run is called the horizontal asymptote.
From the graph, the curve levels off near:
y=2,500
So the number of letters processed per day is trending toward:
2,500
This does not mean the mail center immediately processes exactly 2,500 letters per day. It means that as time continues, the number gets closer and closer to 2,500.
Therefore, the correct answer is:
# ( " B " )
NEW QUESTION # 112
The function P(t)represents the daily profit, in hundreds of dollars, for a hardware store since opening. The graph of P(t)is shown.
How should the maximum value be interpreted?
Answer: D
Explanation:
The graph shows P(t), where:
t= " years since opening "
and
P(t)= " daily profit in hundreds of dollars "
The graph is a downward-opening curve, so its maximum value occurs at the highest point of the graph, also called the vertex.
From the graph, the highest point occurs at approximately:
t=9
So the maximum daily profit happened approximately:
9 " years after opening "
The vertical value at this maximum point is approximately:
P(t)=29
But the graph measures profit in hundreds of dollars, so:
29×100=2900
Therefore, the maximum daily profit was approximately:
$2,900
So the correct interpretation is:
" Approximately 9 years after opening, a maximum daily profit of approximately " $2,900 " was earned. "
NEW QUESTION # 113
The function P(t)represents the weekly profit, in thousands of dollars, for a rental store since opening. The graph of P(t)is shown.
When did the store have its maximum weekly profit?
Answer: A
Explanation:
The graph shows:
P(t)= " weekly profit in thousands of dollars "
where:
t= " years since opening "
The graph is a downward-opening curve, so it has a maximum value at its highest point. In Applied Algebra, the highest point of this kind of polynomial graph is called the vertex.
To answer the question, we need the t-value of the vertex because the question asks when the store had its maximum weekly profit.
From the graph, the highest point occurs between:
t=5
and
t=6
More specifically, it is approximately:
t=5.5
So the store had its maximum weekly profit approximately:
5.5 " years after opening "
NEW QUESTION # 114
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: C
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 # 115
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 # 116
......
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