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| Section | Objectives |
|---|---|
| Topic 1: Exponential Functions | - Interpret inputs and outputs for exponential functions - Interpret concavity for exponential functions - Interpret rates of change for exponential functions |
| Topic 2: Polynomial Functions | - Interpret inputs and outputs for polynomial functions - Interpret rates of change for polynomial functions - Interpret concavity for polynomial functions |
| Topic 3: Validity of Models | - Determine fit - Examine utility - Determine validity |
| Topic 4: Logistic Functions | - Interpret rates of change for logistic functions - Interpret inputs and outputs for logistic functions - Interpret asymptotes for logistic functions |
| Topic 5: Functions and Algebra of Functions | - Derive conclusions based on graphs - Derive conclusions based on data - Derive conclusions based on notation |
| Topic 6: Linear Functions | - Interpret rates of change for linear functions - Interpret inputs and outputs of linear functions |
| Topic 7: Graphical Depictions | - Interpret asymptotes for situations - Interpret concavity for situations - Interpret rates of change for situations - Interpret maximum and minimum for situations - Interpret inputs and outputs for situations |
>> Applied-Algebra Echte Fragen <<
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103. Frage
As sacks are unloaded off a wagon, the total weight of the wagon and sacks changes. Each sack has the same weight. After 5 sacks are removed, the total weight of the wagon and remaining sacks is 135 pounds. After 9 sacks are removed, the total weight is 87 pounds. What is the weight of each sack?
Antwort: C
Begründung:
This situation has a constant rate of change because each sack weighs the same amount. After 5 sacks are removed, the total weight is 135 pounds. After 9 sacks are removed, the total weight is 87 pounds. From 5 to
9 sacks removed is 4 more sacks. Over the same interval, the total weight decreases by 135#87=48 pounds.
Since 4 sacks account for a 48-pound decrease, each sack must weigh 48÷4=12 pounds. This uses the linear idea that equal changes in the input produce equal changes in the output. Therefore, the weight of each sack is
12 pounds, which is answer A.
104. Frage
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?
Antwort: A
Begründung:
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
105. Frage
The number of people auditioning for a game show is expected to be 7 more than the number of people who auditioned last year. The function A(t) can be used to model the situation, where t represents the number of people who auditioned last year and A(t) represents the number of people expected to audition this year.
Which quantity represents the number of people expected to audition this year, given that 440 people auditioned last year?
Antwort: D
Begründung:
In this function-notation problem, the input represents last year's number of people and the output represents this year's expected number. Because this year's number is 7 more than last year's, the rule is A(t)=t+7. The question says 440 people auditioned last year, so the correct input is 440. Substituting gives A(440)
=440+7=447. This means if 440 people auditioned last year, then 447 are expected to audition this year. The notation must place 440 inside the parentheses because that is the input value, and 447 must be written as the output value. The other options reverse the input and output or subtract instead of adding. Therefore, option C is correct.
106. Frage
Based on collected data, the value of a painting can be modeled using the exponential function f(x)=240(1.12) x
. In this case, x represents the number of years since 2005, and f(x) represents the value of the painting in dollars.
Which value represents the average yearly rate of change of the painting's value from 2013 to 2015?
Antwort: A
Begründung:
This problem asks for an average yearly rate of change over a time interval. Since x represents years since
2005, the year 2013 corresponds to x=8, and the year 2015 corresponds to x=10. Use the average rate of change formula:
10#8
f(10)#f(8)
Evaluating the model gives f(8)=240(1.12)
8
#594.23 and f(10)=240(1.12)
10
#745.40. The total change is approximately 151.17 dollars over 2 years. Dividing by 2 gives about 75.59 dollars per year. Since the question asks for the average yearly rate, not the total increase, the correct answer is B.
107. Frage
The number of people, P, in a festival audience is represented by the graph, with the number of hours since the beginning of the festival along the horizontal axis and the size of the audience along the vertical axis.
Point Arepresents an audience size of 402 for the first hour of the festival, or P(0)=402.
Which ordered pair represents a point on the graph?
Antwort: A
Begründung:
This question is about reading an ordered pair from a graph.
An ordered pair has the form:
(x#y)
where:
x= " time in hours "
and
y= " audience size "
From the graph:
Point Ais at approximately (0#402)
Point Bis at (2#401)
Point Cis at (4#403)
Point Dis at (6#406)
Point Eis at approximately (8#410)
Point Fis at (10#408)
Now compare these graph points with the answer choices.
Choice A says:
(2#401)
This matches point Bon the graph exactly.
The other choices do not match the graph:
(4#404)
is incorrect because at x=4, the graph shows about 403, not 404.
(8#409)
is incorrect because at x=8, the graph is about 410, not 409.
(10#407)
is incorrect because at x=10, the graph shows about 408, not 407.
108. Frage
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