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| Section | Objectives |
|---|---|
| Polynomial and Rational Expressions | - Rational Expressions
|
| Foundations of Algebra | - Equations and Inequalities
|
| Exponential and Logarithmic Concepts | - Logarithmic Basics
|
| Linear Functions and Systems | - Systems of Equations
|
| Functions and Graphs | - Function Concepts
|
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NEW QUESTION # 27
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?
Answer: A
Explanation:
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.
NEW QUESTION # 28
The logistic function f(x), whose graph is shown, models the number of people who have created a website account, where xrepresents the number of days since the website started and f(x)represents the number of people who have created an account.
What is one range of values for which the graph is concave down?
Answer: D
Explanation:
For a logistic graph, concavity changes at the inflection point.
Before the inflection point, the graph is usually concave up. This means the function is increasing faster and faster.
After the inflection point, the graph is concave down. This means the function is still increasing, but it is increasing slower and slower.
From the graph, the curve changes concavity around:
x=8
After x=8, the graph begins to level off as it approaches its upper limit.
So one interval where the graph is concave down is:
(8#16)
Therefore, the correct answer is:
# ( " A " )
NEW QUESTION # 29
The graph shows the number of customers, C(t), showing up to a store, where the number of hours since opening is along the horizontal axis and the number of customers showing up to the store each hour is along the vertical axis.
How can the concavity be described from t=6.2to t=10.1?
Answer: A
Explanation:
From t=6.2to about t=8.5, the graph is increasing, but it is becoming less steep as it approaches a local maximum.
That means the number of customers is:
" increasing slower and slower "
After the local maximum, from about t=8.5to t=10.1, the graph begins to decrease and becomes steeper downward.
That means the number of customers is:
" decreasing faster and faster "
So the full description is:
" The number of customers increases slower and slower and then decreases faster and faster. " Therefore, the correct answer is:
# ( " D " )
NEW QUESTION # 30
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 #
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