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| Section | Objectives |
|---|---|
| Polynomial Functions | - Interpret concavity for polynomial functions - Interpret inputs and outputs for polynomial functions - Interpret rates of change for polynomial functions |
| Logistic Functions | - Interpret rates of change for logistic functions - Interpret inputs and outputs for logistic functions - Interpret asymptotes for logistic functions |
| Graphical Depictions | - Interpret concavity for situations - Interpret inputs and outputs for situations - Interpret rates of change for situations - Interpret maximum and minimum for situations - Interpret asymptotes for situations |
| Validity of Models | - Determine validity - Examine utility - Determine fit |
| Linear Functions | - Interpret inputs and outputs of linear functions - Interpret rates of change for linear functions |
| Exponential Functions | - Interpret concavity for exponential functions - Interpret inputs and outputs for exponential functions - Interpret rates of change for exponential functions |
| Functions and Algebra of Functions | - Derive conclusions based on data - Derive conclusions based on notation - Derive conclusions based on graphs |
>> Applied-Algebra Deutsche <<
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92. Frage
The number of registered voters in a district is modeled by a decreasing exponential function, where x represents the number of years since 2005 and f(x) represents the number of registered voters.
Which interval is associated with the slowest average decrease in the number of registered voters?
Antwort: C
Begründung:
A decreasing exponential function falls quickly at first and then levels off over time. The "slowest average decrease" occurs where the graph is flattest, because the output changes by the smallest amount per year.
Earlier intervals, such as 2005 to 2008, occur when the graph is steepest, so those intervals have a faster average decrease. Later intervals occur after the exponential decay has slowed. From the graph, the interval from 2015 to 2025 is farthest to the right and has the least steep downward trend. Therefore, the number of registered voters decreases most slowly during that interval. This is why the correct answer is D.
93. Frage
The function P(t)represents the daily profit, in hundreds of dollars, for a hardware store since opening. The graph of P(t)is shown.
How should the maximum value be interpreted?
Antwort: A
Begründung:
The graph shows P(t), where:
t= " years since opening "
and
P(t)= " daily profit in hundreds of dollars "
The graph is a downward-opening curve, so its maximum value occurs at the highest point of the graph, also called the vertex.
From the graph, the highest point occurs at approximately:
t=9
So the maximum daily profit happened approximately:
9 " years after opening "
The vertical value at this maximum point is approximately:
P(t)=29
But the graph measures profit in hundreds of dollars, so:
29×100=2900
Therefore, the maximum daily profit was approximately:
$2,900
So the correct interpretation is:
" Approximately 9 years after opening, a maximum daily profit of approximately " $2,900 " was earned. "
94. Frage
Consider the graph of x(t) shown. The function represents the number of users, x, watching a live video t hours after 9:00 a.m.
Which interval represents a range of values for which the number of users is decreasing slower and slower?
Antwort: C
Begründung:
To describe "decreasing slower and slower," the graph must be moving downward while becoming less steep.
This means the function values are decreasing, but the rate of decrease is becoming smaller in magnitude. On the graph of x(t), the number of users first increases, then decreases after reaching a local maximum. The interval from t=6.8 to t=7.4 lies on a decreasing part of the curve where the graph is beginning to flatten compared with the steeper earlier decrease. That behavior means the number of users is still going down, but not as quickly as before. The other intervals either occur while the graph is increasing or include behavior that does not consistently match decreasing slower and slower. Therefore, the correct answer is C.
95. Frage
The graph shows the daily practice duration for a musician, where the number of days since the beginning of the month is along the horizontal axis and the number of minutes practiced per day is along the vertical axis.
Based on the graph, what was the practice duration for day 8?
Antwort: B
Begründung:
This question asks us to interpret a value from a graph.
The horizontal axis represents:
Days
The vertical axis represents:
Practice duration in minutes
We need to find the practice duration on day 8.
To do this:
Locate 8 on the horizontal axis.
Move vertically until you reach the blue graph.
Read the corresponding value on the vertical axis.
From the graph, when:
x=8
the blue graph is at:
y=115
So the musician practiced for:
115 minutes
96. Frage
A set of data was gathered and used to create a model for the number of subscribers to a blog. The function model is f(x)=190× # 0.99 #