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| Section | Objectives |
|---|---|
| Topic 1: Linear Functions | - Interpret rates of change for linear functions - Interpret inputs and outputs of linear functions |
| Topic 2: Functions and Algebra of Functions | - Derive conclusions based on data - Derive conclusions based on graphs - Derive conclusions based on notation |
| Topic 3: Polynomial Functions | - Interpret concavity for polynomial functions - Interpret rates of change for polynomial functions - Interpret inputs and outputs for polynomial functions |
| Topic 4: Exponential Functions | - Interpret inputs and outputs for exponential functions - Interpret concavity for exponential functions - Interpret rates of change for exponential functions |
| Topic 5: Logistic Functions | - Interpret asymptotes for logistic functions - Interpret inputs and outputs for logistic functions - Interpret rates of change for logistic functions |
| Topic 6: Validity of Models | - Determine validity - Determine fit - Examine utility |
| Topic 7: Graphical Depictions | - Interpret asymptotes for situations - Interpret maximum and minimum for situations - Interpret concavity for situations - Interpret rates of change for situations - Interpret inputs and outputs for situations |
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質問 # 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?
正解：D
解説：
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 "
質問 # 114
The logistic function f(x), whose graph is shown, models the number of people with a viral infection, where x represents the number of days since the outbreak of the virus and f(x) represents the number of viral infections.
What happens as time progresses from day 9 to day 12?
正解：C
解説：
The graph represents a logistic growth model for viral infections. From day 9 to day 12, the curve is moving upward, so the number of infected people is increasing. During this interval, the graph is also becoming steeper, which means the rate of increase is getting larger. When a function is increasing and its slope is increasing, the correct description is that the quantity increases faster and faster. This interval occurs before the logistic graph begins to level off near its carrying capacity. The choices involving decrease are incorrect because the graph is not going downward. The choice "increases slower and slower" would apply to a later interval where the graph flattens. Therefore, the correct answer is A.
質問 # 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?
正解：C
解説：
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.
質問 # 116
The function F(n) represents the relationship between the number of animals in two enclosures, where n is the number of animals in enclosure A and F is the number of animals in enclosure B. The number of animals in enclosure B is 20 more than the number of animals in enclosure A.
Which function represents this situation?
正解：D
解説：
The function F(n) gives the number of animals in enclosure B.
The input n represents the number of animals in enclosure A.
The problem says enclosure B has 20 more animals than enclosure A. The phrase "20 more than" means we add 20:
F(n)=n+20
For example, if enclosure A had 30 animals, then enclosure B would have:
F(30)=30+20=50
So the function that represents the situation is:
F(n)=n+20
質問 # 117
A company provides internet service to approximately 1,050 customers each year. The table shows the percentage of customers with fiber internet each year since 2020.
Years since 2020 Percent of Customers with Fiber
0 19
1 28
2 40
3 57
What was the approximate number of customers with fiber internet in 2023?
正解：D
解説：
The table gives the percent of customers with fiber internet for each year since 2020.
Since 2023 is:
2023#2020=3
we use the row where:
Years since 2020=3
From the table, the percent of customers with fiber internet in 2023 is:
57%
The company has approximately:
1,050
customers each year.
Now find 57% of 1,050:
0.57×1,050=598.5
The closest answer choice is:
598
So approximately 598 customers had fiber internet in 2023.
Therefore, the correct answer is:
C
質問 # 118
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10年以上のビジネス経験により、当社のApplied-Algebraテストトレントは、顧客の購入体験を非常に重要視していました。電子製品の購入速度を心配する必要はありません。弊社では、Applied-Algebra試験準備の信頼性を長期間にわたって評価および評価し、保証された購入スキームを提案するために尽力しています。
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