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| Section | Objectives |
|---|---|
| Exponential and Logarithmic Concepts | - Logarithmic Basics
|
| Polynomial and Rational Expressions | - Polynomials
|
| Foundations of Algebra | - Equations and Inequalities
|
| Linear Functions and Systems | - Linear Equations
|
| Functions and Graphs | - Function Concepts
|
>> WGU Applied-Algebraファンデーション <<
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質問 # 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?
正解：C
解説：
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 "
質問 # 55
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.
What was the practice duration for day 9, based on the graph?
正解：C
解説：
This question asks us to read and interpret a value from a graph.
The horizontal axis represents:
" Days since the beginning of the month "
The vertical axis represents:
" Practice duration in minutes "
We need to find the practice duration for:
" day " 9
To do this, locate 9on the horizontal axis, move upward to the blue graph, and then read the corresponding value on the vertical axis.
From the graph, the point at day 9is approximately:
127
So the musician practiced for:
127 " minutes "
質問 # 56
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?
正解：C
解説：
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.
質問 # 57
Based on collected data, the number of registered voters in a district can be modeled using the function f(x)=1,300× # 0.92 #