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| Section | Objectives |
|---|---|
| Graphical Depictions | - Interpret maximum and minimum for situations - Interpret asymptotes for situations - Interpret inputs and outputs for situations - Interpret rates of change for situations - Interpret concavity for situations |
| Functions and Algebra of Functions | - Derive conclusions based on data - Derive conclusions based on graphs - Derive conclusions based on notation |
| Linear Functions | - Interpret inputs and outputs of linear functions - Interpret rates of change for linear functions |
| Logistic Functions | - Interpret inputs and outputs for logistic functions - Interpret rates of change for logistic functions - Interpret asymptotes for logistic functions |
| Exponential Functions | - Interpret concavity for exponential functions - Interpret inputs and outputs for exponential functions - Interpret rates of change for exponential functions |
| Polynomial Functions | - Interpret concavity for polynomial functions - Interpret rates of change for polynomial functions - Interpret inputs and outputs for polynomial functions |
| Validity of Models | - Determine fit - Examine utility - Determine validity |
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NEW QUESTION # 108
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: A
Explanation:
The horizontal asymptote describes the long-term behavior of the function. In this problem, the graph shows a decreasing exponential model for the number of licensed sellers. The graph begins near a higher value and then decreases, eventually leveling off near 300. This means the number of licensed sellers approaches 300 over time. It does not mean the number necessarily becomes exactly 300 at 21 months, and it does not mean the sellers increase back to the initial value. The initial value is separate from the horizontal asymptote. Since the graph levels off around 300, the correct interpretation is that in the long run, the number of licensed sellers nears 300. Therefore, the answer is C.
NEW QUESTION # 109
The function P(t)represents the yearly profit, in millions of dollars, for a streaming service since opening. The graph of P(t)is shown.
What is the correct interpretation of the maximum value?
Answer: B
Explanation:
The graph represents yearly profit as a function of time:
P(t)= " yearly profit "
where:
t= " years since opening "
The graph is a downward-opening curve, so its maximum value occurs at the highest point, also called the vertex.
From the graph, the highest point occurs at approximately:
t=10.5
So the maximum yearly profit happened approximately:
10.5 " years after opening "
The vertical axis measures yearly profit in millions of dollars. From the graph, the maximum value is approximately:
1.41
Since the units are millions of dollars:
1.41×1,000,000=1,410,000
So the maximum yearly profit was approximately:
$1,410,000
Therefore, the correct answer is:
# ( " C " )
NEW QUESTION # 110
The growth of an animal population is shown in the graph. The instantaneous rate of change at point Pis 3.74.
Which interpretation of the instantaneous rate of change is correct?
Answer: C
Explanation:
The graph shows population in thousands, and the horizontal axis represents:
" years since 1995 "
Point Pis located at approximately:
x=12
Since xrepresents years since 1995:
1995+12=2007
So point Pcorresponds to the year:
2007
The instantaneous rate of change at point Pis:
3.74
Because the vertical axis is measured in thousands, this means:
3.74 " thousand animals per year "
Convert thousands to actual animals:
3.74×1000=3740
So in 2007, the population was increasing by approximately:
3,740 " animals per year "
NEW QUESTION # 111
The number of members of a religious organization can be modeled using the logistic function f(x), where xrepresents the number of years since the organization was started and f(x)represents the number of members.
The graph of f(x)is shown.
What is one range of values for which the graph is concave down?
Answer: A
Explanation:
The graph is a logistic growth curve.
A logistic growth curve has two main concavity regions:
" concave up before the inflection point "
and
" concave down after the inflection point "
From the graph, the function increases faster and faster until about:
x=6
After x=6, the graph continues increasing, but it begins to flatten out. That means the number of members is increasing slower and slower.
This is concave down behavior.
Therefore, one interval where the graph is concave down is:
(6#11)
So the correct answer is:
# ( " D " )
NEW QUESTION # 112
The populations, in thousands, of two towns are shown in the graph, where the horizontal axis measures the time in years.
Which town's population is growing at a faster rate?
Answer: C
Explanation:
This question asks which town's population is growing at a faster rate.
Since both population graphs are straight lines, we compare their slopes.
The slope of a line represents the rate of change:
" slope " = " change in population " / " change in time "
From the graph:
Town A starts at about 8.0thousand people and increases at a rate of about 1.0thousand people per year.
Town B starts at about 5.5thousand people and increases at a rate of about 1.3thousand people per year.
Even though Town A starts with a larger population, the question asks about the growth rate, not the starting population.
Compare the rates:
1.3 > 1.0
So Town B is growing faster than Town A.
NEW QUESTION # 113
......
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