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| Section | Objectives |
|---|---|
| Topic 1: Graphical Depictions | - Interpret inputs and outputs for situations - Interpret rates of change for situations - Interpret maximum and minimum for situations - Interpret concavity for situations - Interpret asymptotes for situations |
| Topic 2: Logistic Functions | - Interpret asymptotes for logistic functions - Interpret inputs and outputs for logistic functions - Interpret rates of change for logistic functions |
| Topic 3: Functions and Algebra of Functions | - Derive conclusions based on notation - Derive conclusions based on data - Derive conclusions based on graphs |
| Topic 4: Exponential Functions | - Interpret inputs and outputs for exponential functions - Interpret rates of change for exponential functions - Interpret concavity for exponential functions |
| Topic 5: Validity of Models | - Examine utility - Determine fit - Determine validity |
| Topic 6: Linear Functions | - Interpret rates of change for linear functions - Interpret inputs and outputs of linear functions |
| Topic 7: Polynomial Functions | - Interpret rates of change for polynomial functions - Interpret inputs and outputs for polynomial functions - Interpret concavity for polynomial functions |
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NEW QUESTION # 105
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: A
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 # 106
The logistic function f(x), whose graph is shown, models the number of people with a viral infection, where x represents the number of days since the outbreak of the virus and f(x) represents the number of viral infections.
What happens as time progresses from day 9 to day 12?
Answer: C
Explanation:
The graph represents a logistic growth model for viral infections. From day 9 to day 12, the curve is moving upward, so the number of infected people is increasing. During this interval, the graph is also becoming steeper, which means the rate of increase is getting larger. When a function is increasing and its slope is increasing, the correct description is that the quantity increases faster and faster. This interval occurs before the logistic graph begins to level off near its carrying capacity. The choices involving decrease are incorrect because the graph is not going downward. The choice "increases slower and slower" would apply to a later interval where the graph flattens. Therefore, the correct answer is A.
NEW QUESTION # 107
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: C
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 # 108
A researcher collected data on the number of annual bear sightings in a region over time. The results are shown in the scatterplot. A regression function is graphed with r