Applied Algebra FX01 Exam (C957)
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Free Applied Algebra FX01 Exam (C957) Questions
A small pond contains 12 units of dissolved oxygen in a fixed volume of water. At time t = 0, a quantity of organic waste is introduced into the pond. The oxygen concentration, y, is shown in t weeks in the graph below.
As time passes, what will be the ultimate concentration of oxygen in the pond?
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The oxygen concentration stabilizes near 5 units.
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The oxygen concentration stabilizes near 12 units.
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The oxygen concentration stabilizes near 24 units.
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The oxygen concentration stabilizes near 42 units.
Explanation
Correct answer:
The oxygen concentration stabilizes near 12 units.
Explanation
This is because the oxygen concentration graph flattens between 11 and 12 but seems to stop the increment at 12 units.
Why other options are wrong:
“The oxygen concentration stabilizes near 5 units” This is incorrect since the horizontal asymptote is between 11 and 12 units.
“The oxygen concentration stabilizes near 24 units” This is incorrect since the oxygen level does not reach this level.
“The oxygen concentration stabilizes near 42 units” This is incorrect since the oxygen level does not reach this level.
The rate of profit in the business sector of the United States from 1929 to 1962 is illustrated by the function R in the graph below. Point A represents a rate of profit of 0.31 in the year 1929, or R(1929) = 0.31.
What can be concluded about this function?
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Point B represents R(1932) = 0.2.
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Point D represents R(1941) = 0.37.
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Point I represents R(1961) = 0.3.
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Point E represents R(1945) = 0.5.
Explanation
Solution:
Rechecking the options;
Point B represents R(1932) = 0.2
Point D represents R(1941) = 0.32.
Point I represents R(1961) = 0.3.
Point E represents R(1945) = 0.49
From the graph point B is not 1932, hence it can be concluded that Point I represents R(1961) = 0.3.
Correct answer:
Point I represents R(1961) = 0.3.
Why other options are wrong:
“Point B represents R(1932) = 0.2.” From the graph point B is not 1932
“Point D represents R(1941) = 0.37.” Point D represents R(1941) = 0.32.
“Point E represents R(1945) = 0.5.” Point E represents R(1945) = 0.49
A technology company is developing an accelerometer and collects the data in the following graph that measures the position of a remote control car with respect to time in seconds.
What is the concavity of each patterned section of the graph?
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A is increasing slower and slower. B is decreasing slower and slower and then increasing faster and faster. C is increasing faster and faster. D is decreasing faster and faster.
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A is increasing slower and slower. B is decreasing faster and faster and then decreasing slower and slower. C is increasing faster and faster. D is decreasing slower and slower.
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A is increasing faster and faster. B is decreasing slower and slower and then increasing slower and slower. C is increasing slower and slower. D is decreasing faster and faster.
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A is increasing faster and faster. B is decreasing faster and faster and then decreasing slower and slower. C is increasing slower and slower. D is decreasing slower and slower.
Explanation
Correct answer:
A is increasing faster and faster. B is decreasing slower and slower and then increasing slower and slower. C is increasing slower and slower. D is decreasing faster and faster.
Why other are wrong:
“A is increasing slower and slower. B is decreasing slower and slower and then increasing faster and faster. C is increasing faster and faster. D is decreasing faster and faster.” A is not increasing slower and slower since the rate of change for A is faster and faster as y changes more faster than in the x axis.
“A is increasing slower and slower. B is decreasing faster and faster and then decreasing slower and slower. C is increasing faster and faster. D is decreasing slower and slower.” A is not increasing slower and slower since the rate of change for A is faster and faster as y changes more faster than in the x axis.
“A is increasing faster and faster. B is decreasing faster and faster and then decreasing slower and slower. C is increasing slower and slower. D is decreasing slower and slower.” B is not decreasing faster and faster and then decreasing slower and slower rather it decreases slower and slower and then increases slower and slower.
A consulting firm conducts a study to determine how much revenue a company would make on a new item it is bringing to market based on the selling price of the item. The graph below shows the firm's data, along with the best-fit curve. The data and curve have an r² value of 0.98, and the curve uses the equation y = -0.98x² + 74.56x - 38.48.
The firm concludes that in order to maximize revenue from selling this new item, the company should sell the item for $38. Is this a valid conclusion?
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Yes, this is a valid conclusion because the model appropriately fits the data, and the model guarantees that selling the item for $38 yields a higher revenue than any other selling price.
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No, this is not a valid conclusion because the firm never collected data on a selling price of $38.
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No, this is not a valid conclusion because the data contain outliers, which cause predictions made with the best-fit curve to be inaccurate.
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Yes, this is a valid conclusion because the model appropriately fits the data, and the model predicts that the maximum revenue is obtained when the selling price is around $38.
Explanation
Correct answer:
Yes, this is a valid conclusion because the model appropriately fits the data, and the model predicts that the maximum revenue is obtained when the selling price is around $38.
Explanation
The correct answer is that the model predicts that the maximum revenue is obtained when the selling price is around $38. The equation used in the curve suggests a quadratic relationship, with the vertex representing the maximum revenue point. Even though data for exactly $38 was not collected, the model, with a strong r² value of 0.98, provides a reliable prediction. Therefore, the model's prediction of the optimal price point is valid, even without direct data at that price.
Why others are wrong:
“No, this is not a valid conclusion because the firm never collected data on a selling price of $38.” This statement is incorrect because the model's purpose is to predict revenue for any price, even if that specific price point wasn't included in the data. The high r² value (0.98) indicates that the model fits the data well and is reliable for predictions. Thus, the lack of direct data at $38 does not invalidate the conclusion.
“No, this is not a valid conclusion because the data contain outliers, which cause predictions made with the best-fit curve to be inaccurate.” The graph does not appear to show significant outliers that would undermine the model's accuracy. Moreover, an r² value of 0.98 strongly suggests that the model fits the data extremely well, minimizing concerns about outliers affecting the prediction.
“Yes, this is a valid conclusion because the model appropriately fits the data, and the model guarantees that selling the item for $38 yields a higher revenue than any other selling price.” This statement is mostly correct but slightly misworded. The model does not "guarantee" revenue at $38; it predicts it based on the best-fit curve. The use of "guarantee" may imply certainty beyond what the model can provide. A better phrasing is: "the model predicts that the maximum revenue is obtained when the selling price is around $38.
The number (in millions) of cable TV subscriptions, N, in years since 1980, x, is given by the graph below, where x = 0 corresponds to the year 1980.
What is true about the rate at which TV subscriptions change?
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Each year the rate at which subscriptions grow is the same.
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The increase in subscriptions between 1980 and 1981 is less than the increase in subscriptions between 1985 and 1986.
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The increase in subscriptions between 1980 and 1981 is more than the increase in subscriptions between 1985 and 1986.
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Each year the rate at which subscriptions grow increases.
Explanation
Solution:
Since the function is governed by a straight line the rate of increase is the same since the gradient of a straight line is the same in all points.
Correct answer:
Each year the rate at which subscriptions grow is the same.
Why the other answers are wrong:
“The increase in subscriptions between 1980 and 1981 is less than the increase in subscriptions between 1985 and 1986.” The solution is wrong since the rate of increase is the same.
“The increase in subscriptions between 1980 and 1981 is more than the increase in subscriptions between 1985 and 1986.” The solution is wrong since the rate of increase is the same.
“Each year the rate at which subscriptions grow increases.” The rate is constant hence the solution is wrong.
The function g in the graph below plots the number of information technology employees (in thousands) in the United States from the years 2000 to 2011 (t).
Which conclusion can be made based on this graph?
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There were 1,200 employees in the year 2004.
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There were 1,200,000 employees in the year 2005.
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There were 1,400,000 employees in the year 2007.
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There were 1,400 employees in the year 2008.
Explanation
Correct answer:
There were 1,200,000 employees in the year 2005.
Solution:
From the function in the graph which is in thousand, there were 1,200,000 employees in the year 2005.
Why others options are wrong:
“There were 1,200 employees in the year 2004.” The graph is in thousand hence the employees in 2004 were 1,200,000 not 1,200.
“There were 1,400,000 employees in the year 2007.” This value is almost true but from the graph the line has not touched the point represented by 1,400,000 and 2007.
“There were 1,400 employees in the year 2008.” The year with the least employees is above this value as the values are presented in 1000 employees.
The revenue R generated from selling x products is modeled by the function:
R(x) = 200x − 5x2
At what number of products, x, will the revenue be maximized?
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10 products
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20 products
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30 products
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40 products
Explanation
Correct Answer:
20 products
Solution:
The revenue function R(x) = 200x − 5x2 is a quadratic equation. The maximum revenue occurs at the vertex, calculated as:
Why Other Options Are Wrong:
"10 products" Incorrect because the vertex is at x = 20, not x = 10.
"30 products" Incorrect because the revenue begins to decline past x = 20.
"40 products" Incorrect because x = 40 is well beyond the point of maximum revenue.
The data in the scatterplot represents the number of monthly train crossings at a particular intersection over time.
Which type of function should be used to model the data?
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Logistic
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Linear
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Exponential
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Polynomial
Explanation
Explanation
The scatterplot shows a rapid decrease in the number of monthly train crossings that then levels off. This suggests an exponential decay pattern, where the values initially decrease sharply but then approach a lower limit, making an exponential function the most suitable model.
Correct answer
Exponential
In growth scenarios in both biology and business, it is very common for the observed aspect to increase faster and faster before slowing down and increasing slower and slower. When growth slows like this it is called plateauing. This behavior can repeat over and over again. Which graph could be a possible model for this behavior of increasing faster and faster and then increasing slower and slower and then repeating?
Explanation
Correct answer:
(C)The correct graph is the third graph.
Explanation
The third graph clearly shows multiple "S-shaped" curves (sigmoid growth patterns) that repeat. Each segment starts with a rapid increase (steep slope), followed by a slowdown in growth (flattening slope), then another rapid increase — matching the pattern of plateauing and restarting growth cycles typical in biological and business scenarios.
Why others are wrong:
The first graph increases slower and slower before increasing faster and faster before slowing down.
The second graph increases slower and slower before increasing faster and faster then this phenomenon repeats.
A company has opened a new factory to produce more parts for its production. The board expects profits to increase faster and faster over time. Which graph appropriately models this situation? Assume the x-axis corresponds to time after opening the factory in months, and the y-axis corresponds to profit in thousands of dollars.
Explanation
Explanation
The correct option is C. This is because it's the only graph that is only increasing without decreasing.
Correct answer
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Frequently Asked Question
This course covers a variety of algebraic concepts, including solving linear equations and inequalities, quadratic equations, graphing functions, systems of equations, exponents, polynomials, and real-world applications of algebra.
Yes, all practice questions and study materials are meticulously updated and aligned with the 2025 standards to ensure students are prepared for current academic and professional requirements.
The course includes practical scenarios such as calculating interest, analyzing business data, optimizing resources, and modeling real-world situations with algebraic equations and graphs.
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You can prepare by reviewing the practice questions, studying the provided rationales, working on real-world application problems, and using the exam-focused blueprints included in the course materials.
Yes, a graphing calculator is highly recommended, as it is essential for solving complex problems, graphing functions, and visualizing algebraic concepts.
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