Applied Algebra FX01 Exam (C957)
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Free Applied Algebra FX01 Exam (C957) Questions
A population of 20 endangered bears was released into a wilderness sanctuary in 2000. Biologists estimated that the bear population would grow as projected in the graph below.
How long will it take for the bear population to reach 100 bears if these projections are correct?
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About 160 years
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About 96 years
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About 100 years
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About 78 years
Explanation
Solution:
From the graph on the y axis at 100 the corresponding point on the x axis is below 80 years, about 78 years.
Correct answer:
About 78 years.
Why other are wrong:
“About 160 years” Given the growth follows exponential distribution this value is higher than the expected value since the population will be 160 after 100 years.
“About 96 years” From the graph after about 96 years the population will be above 140 approximately 155.
“Abou 100 years” From the graph, after 100 years the population will be 160.
Below is a table of collected data where P(t) is the number of bacteria at a given time and t is the time measured in hours.
Which exponential function would model this situation well?
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P(t) = 332e0.1528t
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P(t) = 300e0.0507t
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P(t) = 332e0.0507t
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P(t) = 300e0.1528t
Explanation
Solution:
Step 1: Analyze the characteristics of exponential growth
Initial value P(0) = 300
The function should have form P(t) = Po e(rt) where:
P₀ is the initial value (when t = 0)
r is the growth rate
Step 2: Compare the given functions with the data
We need P₀ = 300 (initial value)
Any function starting with 332 can be eliminated
Looking at the growth pattern, we need the function that best fits the data points
Step 3: Calculate the growth rate using the data Using t = 0 and t = 6 data points:
P(0) = 300
P(6) = 404
Using the formula: P(t) = Po e(rt)
404 = 300 e(6r)
404/300 = e(6r)
ln(404/300) = 6r
ln(1.3467) = 6r
0.297/6 ≈ 0.0507
Step 4: Verify the function with middle points Using P(t) = 300e^0.0507t:
When t = 2: 300e(0.0507×2) ≈ 332 (matches data)
When t = 4: 300e(0.0507×4) ≈ 366 (matches data)
Correct Answer:
P(t) = 300e0.0507t
Why the other options are wrong:
"P(t) = 332e0.1528t ": This is incorrect because the initial value (332) doesn't match P(0) = 300.
"P(t) = 332e0.0507t:” This is incorrect because the initial value (332) doesn't match P(0) = 300.
“P(t) = 300e0.1528t:” This is incorrect because the growth rate of 0.1528 would result in values much larger than those shown in the data table.
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. What was the approximate number of customers with fiber internet in 2023?
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420
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452
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598
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630
Explanation
Explanation
The year 2023 corresponds to 3 years since 2020. According to the table, 57% of customers had fiber internet at that time. To find the approximate number of customers, multiply 57% by 1,050: 0.57 * 1050 = 598.5. Rounding to the nearest whole number gives approximately 598 customers.
Correct answer
598
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.
A theme park charges admission based on age where P() is the price function in dollars. The pricing rules are:
Children under 5 get in free
Ages 5-12 pay $25 plus $2 for each year of age
Ages 13-17 pay a flat rate of $50
Ages 18+ pay $60 minus $1 for each year over 65 (if applicable)
What is the correct function notation to represent the admission price for a 72-year-old visitor?
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P(72) = 53
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P(53) = 72
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P(72) = 47
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P(47) = 72
Explanation
Correct Answer:
P(72) = 47
Explanation:
For ages 18+ with senior discount, the function can be written as:
P(x) = 60 - (x - 65) if x > 65 where x is the age.
For a 72-year-old visitor:
P(72) = 60 - (72 - 65) = 60 - 7 = 47
Thus, the correct representation is P(72) = 47.
Why the other options are wrong:
"P(72) = 53": This is incorrect because it doesn't properly apply the senior discount formula. It appears to only subtract half of the years over 65.
"P(53) = 72": This is incorrect for two reasons:
It reverses the input and output - P(x) represents the price for age x, not vice versa
Age 53 would actually result in P(53) = 60, as it's in the adult category with no senior discount
"P(47) = 72": This is incorrect because:
It reverses the relationship between age and price
A 47-year-old would pay the standard adult price of $60
72 is not a possible price output given the pricing rules.
The given function represents the price of a commodity, ( p ), in dollars, based on the number of months, ( m ), since the beginning of 2020. The function is:
p(m) = 5m + 5
What is the average rate of change of the price over the interval m = 1 to m = 10?
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5
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5.91
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32.5
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45
Explanation
Explanation
The average rate of change of a function over an interval is given by the formula:
p(m2) - p(m1)/m2 - m1
Here, m1 = 1 ) and m2 = 10.
First, calculate p(1) and p(10):
p(1) = 5(1) + 5 = 10
p(10) = 5(10) + 5 = 55
Now, calculate the average rate of change:
p(10) - p(1)/10 - 1 = 55 - 10/9 = 5
Correct answer
5
An employee works at a large department store and gets an employee discount on any purchases made at the store. The price the employee pays can be modeled by the function D(c) = c - 0.15c, where c is the original price of the item in dollars and D is the discounted price of the item. What does this model represent in the context of the problem?
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The employee pays $c after receiving an 15% discount for an item that originally cost $D.
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The employee pays $0 after receiving a 15% discount for an item that originally cost $c.
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The employee pays $D after receiving an 85% discount for an item that originally cost $c.
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The employee pays $c after receiving a 15% discount for an item that originally cost $D.
Explanation
Correct Answer:
The employee pays D after receiving a 85% discount for an item that originally cost $c.
Explanation:
The function D(c)=c − 0.15c calculates the discounted price (D) of an item. The term 0.15c represents a 15% discount off the original price (c), so the total price the employee pays is 85% of the original price:
D(c) = c(1−0.15) = 0.85c
This means the employee pays D, the discounted price, which is 85% of the original price c, after receiving a 15% discount.
Why the other options are wrong:
"The employee pays c after receiving an 85% discount for an item that originally cost D": This is incorrect because the employee pays D, not c, after the discount is applied. Additionally, the discount is 15%, not 85%.
"The employee pays $0 after receiving a 15% discount for an item that originally cost c": This is incorrect because a 15% discount does not reduce the price to $0. The price is reduced to 85% of the original price.
"The employee pays D after receiving an 85% discount for an item that originally cost c": This is incorrect because the discount is 15%, not 85%.
A college is modeling student enrollment growth using the function:
E(t) = 1,000(1.05)t
where E(t) is the number of students enrolled t years after the college opened. How many students are enrolled after 3 years?
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1,150 students
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1,200 students
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1,250 students
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1,276 students
Explanation
Correct Answer:
1,276 students
Solution:
Substitute t = 3 into the equation:
E(3) = 1,000(1.05)3
= 1,000(1.157625)
≈ 1,276
Why Other Options Are Wrong:
"1,150 students" Incorrect because this underestimates the number of students after 3 years.
"1,200 students" Incorrect because this is slightly lower than the calculated value.
"1,250 students" Incorrect because this underestimates the enrollment growth.
The function f(n) represents the relationship between the distances traveled by two vehicles, where nnn is the distance traveled by vehicle A and f is the distance traveled by vehicle B. The distance traveled by vehicle B is 17 more than the distance traveled by vehicle A. Which function represents this situation?
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f(n) = n − 17
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f(n) = n/17
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f(n) = 17n
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f(n) = n + 17
Explanation
Explanation
The phrase “17 more than” indicates that vehicle B’s distance is found by adding 17 to the distance traveled by vehicle A. Since nnn represents vehicle A’s distance, adding 17 gives the correct expression for vehicle B. The function must therefore be written as n + 17.
Correct answer
n + 17
Two companies have been trying to lower their travel costs since January of last year (which corresponds to x = 0). One company, Endathon, has modeled its reduction in travel costs using the function S(x) = 115e-0.01x, where S measures the travel costs in thousands and x measures time in months. The second company, Bullzai, has modeled its reduction in travel costs using the function G(x) = 120e-0.02x. Below are the graphs of the two functions, with Endothon's graph shown as the solid curve and Bullzai's graph as the dashed curve.
Based on this graph, which company had lower travel costs as of January of this year?
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Endathon, since its costs are about $94,000 compared to about $102,000 for Bullzai.
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Bullzai, since its costs are about $94,000 compared to about $102,000 for Endathon.
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Endathon, since its costs are about $90,000 compared to about $100,000 for Bullzai.
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Bullzai, since its costs are about $90,000 compared to about $100,000 for Endathon.
Explanation
Solution:
Since it is as for January this year this corresponds to the 13th month in the graph.
Using the given equation: For Endathon S(x) = 115e-(0.01 * 13)
= 100.98
≈ $100 thousand
For Bullzai G(x) = 120e-(0.02 * 13)
= 92.53
≈ $92 thousand
The company that had lower travel costs as of January of this year was Bullzai.
Correct answer:
Bullzai, since its costs are about $90,000 compared to about $100,000 for Endathon.
Why others are wrong:
“Endathon, since its costs are about $94,000 compared to about $102,000 for Bullzai.” As it can be seen in the graph Bullzai had the lowest cost.
“Bullzai, since its costs are about $94,000 compared to about $102,000 for Endathon.” Endathon had a cost of approximately $100,000 as seen from the equation and not $102,000.
“Endathon, since its costs are about $90,000 compared to about $100,000 for Bullzai.” As it can be seen in the graph Bullzai had the lowest cost.
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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.
Yes, each practice question comes with step-by-step rationales to explain the correct answers and address common mistakes, helping students develop a deeper understanding of the material.
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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