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| Section | Objectives |
|---|---|
| Exponential and Logarithmic Concepts | - Exponential Functions
|
| Linear Functions and Systems | - Linear Equations
|
| Polynomial and Rational Expressions | - Polynomials
|
| Foundations of Algebra | - Equations and Inequalities
|
| Functions and Graphs | - Graphing Functions
|
>> Latest Applied-Algebra Practice Questions <<
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NEW QUESTION # 54
The number of letters processed daily at a mail center is modeled by the decreasing exponential function shown in the graph.
What is the long-term trend in the number of letters processed per day, based on the equation of the horizontal asymptote?
Answer: B
Explanation:
The graph shows a decreasing exponential function.
In Applied Algebra, a decreasing exponential function may approach a fixed value over time. This fixed value is called the horizontal asymptote.
The horizontal asymptote represents the long-term value that the function gets closer and closer to, but does not necessarily cross or reach exactly.
From the graph, the curve decreases quickly at first, then begins to level off near:
y=1,000
This means that as time continues, the number of letters processed per day approaches:
1,000
So the long-term trend is that the mail center will process about:
1,000 " letters per day "
NEW QUESTION # 55
The value of a collectible coin can be modeled by F(t), where t represents years since the number of years since the coin was found, and the vertical axis represents the value, in thousands of dollars.
How is the value of the coin changing over time based on the graph?
Answer: A
Explanation:
The graph shows the value of the coin increasing over time. Since the curve rises from left to right, the value is not decreasing. The graph also becomes steeper as time increases, which means the rate of increase is getting larger. In Applied Algebra, when a graph is increasing and its slope is increasing, the quantity is described as increasing faster and faster. This is typical of exponential growth, where values grow by a repeated percent or factor rather than by a constant amount. The choices involving decreasing are incorrect because the graph moves upward. The choice "increasing slower and slower" would require the graph to flatten, which it does not. Therefore, the correct answer is B.
NEW QUESTION # 56
A music student attempted to learn a difficult new song. Each day, the student would play the song and be scored on their performance. The graph shows the results.
What was the average daily change in performance from day 16 to day 20?
Answer: C
Explanation:
The average daily change is the average rate of change over the interval from day 16 to day 20. From the graph, the performance score at day 16 is approximately 30.1, and the score at day 20 is approximately 57.6.
Use the formula
x
2
#x
1
y
2
#y
1
Substituting gives
20#16
57.6#30.1
The numerator is 27.5, and the denominator is 4, so the average daily change is 27.5/4=6.875, which rounds to 6.88. This means the performance score increased by an average of about 6.88 points per day over the interval. Therefore, the correct answer is B.
NEW QUESTION # 57
A factory mixes two colors, red and yellow, to create a dye.
The graph shows the relationship between the amounts of each dye, where rrepresents the amount of red dye and yrepresents the amount of yellow dye.
What is the correct interpretation of the rate of change?
Answer: D
Explanation:
The graph shows a linear relationship between the amount of red dye, r, and the amount of yellow dye, y.
The rate of change of a line is the slope:
" slope " =( " change in " y)/( " change in " r)
From the graph, the line goes through the origin and rises steeply. A clear point on the line is approximately:
(2#9)
This means when the amount of red dye is 2gallons, the amount of yellow dye is 9gallons.
So the rate of change is:
9/2
That means for every 2gallons of red dye, the factory uses 9gallons of yellow dye.
The relationship can be written as:
y=9/2 r
So the correct interpretation is:
" The amount of yellow dye must be " 9/2 " of the amount of red dye. "
Therefore, the correct answer is:
# ( " A " )
NEW QUESTION # 58
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: A
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 # 59
......
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