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| Section | Weight | Objectives |
|---|---|---|
| Exponents, Radicals, and Quadratic Relationships | 15% | - Basic quadratic graphs - Simplifying radical expressions - Properties of exponents - Solving quadratic equations |
| Graphing and Functions | 25% | - Slope and equations of lines - Function notation and evaluation - Coordinate plane and plotting points - Linear functions and their graphs |
| Systems of Equations and Inequalities | 15% | - Solving by substitution and elimination - Applications of systems - Graphical solutions |
| Algebraic Expressions and Operations | 20% | - Order of operations - Variables, constants, and coefficients - Simplifying and evaluating expressions - Operations with polynomials |
| Linear Equations and Inequalities | 25% | - Real-world applications - Solving and graphing inequalities - Solving single-variable equations |
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NEW QUESTION # 22
The function N(t)models the number of subscribers to a virtual newsletter over time. The graph of N(t)is shown. The horizontal axis represents the number of years since the newsletter started, and the vertical axis represents the number of subscribers, in thousands.
How is the number of subscribers changing over time based on the graph?
Answer: A
Explanation:
The graph shows an increasing exponential curve.
The number of subscribers is going up as time passes, so the function is increasing.
Also, the graph becomes steeper as time increases. This means the rate of increase is getting larger.
So the number of subscribers is:
" increasing faster and faster "
This is a key feature of exponential growth.
NEW QUESTION # 23
The graphed function n(t)represents the number of people, n, at a park thours after 8:00 a.m. The plotted points Aand Bhave coordinates (2#110)and (6#182).
Which statement gives the correct interpretation of the average rate of change of the number of people over the interval from point Ato point B?
Answer: D
Explanation:
The average rate of change measures how much the output changes per one unit of input.
Here:
t= " hours after 8:00 a.m. "
and
n(t)= " number of people at the park "
The two given points are:
A=(2,110)
and
B=(6,182)
This means:
At t=2hours after 8:00 a.m., there were 110people at the park.
At t=6hours after 8:00 a.m., there were 182people at the park.
Now calculate the average rate of change:
" Average rate of change " =(182-110)/(6-2)
=72/4
=18
Because the value is positive, the number of people is increasing.
So the correct interpretation is:
" The number of people at the park increases at an average rate of 18 people per hour. "
NEW QUESTION # 24
As regulations change, the number of licensed sellers of a product decreases. The graph models the change in the number of licensed sellers over time.
What does the horizontal asymptote mean?
Answer: D
Explanation:
The graph shows a decreasing exponential model.
The vertical axis represents:
" Licensed sellers "
The horizontal axis represents:
" Time in years "
The graph starts near 700 licensed sellers and decreases over time. However, it does not appear to decrease all the way to 0. Instead, it levels off near:
y=100
That horizontal line is the horizontal asymptote.
A horizontal asymptote represents the long-term value the function approaches as time continues.
So the correct interpretation is:
" In the long run, the number of licensed sellers nears 100. "
Therefore, the correct answer is:
# ( " C " )
NEW QUESTION # 25
The function P(t) represents the yearly profit, in thousands of dollars, for a virtual store since opening. The graph of P(t) is shown.
What is the time at which the store reached the maximum yearly profit?
Answer: D
Explanation:
The maximum value of a graph is the highest output value the function reaches. Since P(t) represents yearly profit, the maximum value occurs where the store earns its greatest yearly profit. The graph is a downward- opening curve, so its highest point is the vertex. To answer the question, we need the t-value of the vertex, not the profit amount. From the graph, the highest point occurs between 4 and 5 years after opening, closest to 4.5 years. This means the virtual store reached its maximum yearly profit approximately 4.5 years after it opened.
The later values decrease after the vertex, so options involving 7.5 or 14 years are not correct. Therefore, the correct answer is B.
NEW QUESTION # 26
The figure shows the graph of p(t), which represents the number of people, p, at a gym thours after 7:00 a.m.
How should the concavity between t=1.3and t=3.4be interpreted?
Answer: B
Explanation:
The graph represents:
p(t)= " number of people at the gym "
where:
t= " hours after 7:00 a.m. "
The question asks about the concavity of the graph between:
t=1.3
and
t=3.4
On this interval, the graph is still going upward, so the number of people is increasing.
However, the graph is beginning to flatten as it approaches its highest point. That means the slope is positive, but the slope is getting smaller.
In other words:
" The number of people is increasing, but at a slower rate. "
This is called concave down behavior. For a concave down graph that is increasing, the correct interpretation is:
" increasing slower and slower "
Therefore, the correct answer is:
# ( " C " )
NEW QUESTION # 27
......
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