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| Section | Objectives |
|---|---|
| Topic 1: Logistic Functions | - Interpret inputs and outputs for logistic functions - Interpret rates of change for logistic functions - Interpret asymptotes for logistic functions |
| Topic 2: Polynomial Functions | - Interpret concavity for polynomial functions - Interpret rates of change for polynomial functions - Interpret inputs and outputs for polynomial functions |
| Topic 3: Validity of Models | - Examine utility - Determine fit - Determine validity |
| Topic 4: Linear Functions | - Interpret rates of change for linear functions - Interpret inputs and outputs of linear functions |
| Topic 5: Exponential Functions | - Interpret rates of change for exponential functions - Interpret inputs and outputs for exponential functions - Interpret concavity for exponential functions |
| Topic 6: Functions and Algebra of Functions | - Derive conclusions based on graphs - Derive conclusions based on data - Derive conclusions based on notation |
| Topic 7: Graphical Depictions | - Interpret asymptotes for situations - Interpret rates of change for situations - Interpret maximum and minimum for situations - Interpret concavity for situations - Interpret inputs and outputs for situations |
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NEW QUESTION # 38
The graph shows the number of trees sold by a nursery, where the number of days since the beginning of the month is along the horizontal axis and the number of trees sold per day is along the vertical axis. The greatest number of trees are sold when the temperature is over 70°F.
When was the temperature likely over 70°F?
Answer: C
Explanation:
The problem states that the greatest number of trees are sold when the temperature is over 70°F. Therefore, we need to identify the days on the graph when tree sales are highest. The graph shows two major peaks in the number of trees sold per day. These peaks occur around day 2 and day 10. Since higher tree sales are linked to temperatures over 70°F, those two days are the most likely days when the temperature exceeded 70°F. Day 6 appears near a low point, so it is not likely associated with high temperature based on the given relationship.
Day 12 also does not match the main peaks. Therefore, the correct answer is C.
NEW QUESTION # 39
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: D
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 # 40
A team was assembled at a manufacturing plant in order to boost productivity. The team was tasked with producing as many widgets each day as possible. The results are shown in the graph.
What is the correct interpretation of the average rate of change from day 6 to day 14?
Answer: C
Explanation:
The graph models the number of widgets the team can produce each day.
The horizontal axis represents:
" days "
The vertical axis represents:
" widgets "
The graph gives two labeled points:
(6#3.4)
and
(14#23)
The average rate of change is:
" change in widgets " / " change in days "
Substitute the values:
(23-3.4)/(14-6)
=19.6/8
=2.45
Rounded to the nearest tenth:
2.5
This means the team increased production by an average of approximately:
2.5 " widgets each day "
Therefore, the correct answer is:
# ( " B " )
NEW QUESTION # 41
Through a local marketplace, a person makes livestock feeders to sell. The graph shows the functions modeling the cost and revenue.
What is the minimum number of livestock feeders that must be sold in order for the revenue to cover the costs?
Answer: C
Explanation:
This question asks for the break-even point, which is the point where:
Revenue=Cost
On the graph:
The solid blue line represents revenue.
The dashed blue line represents cost.
The revenue line starts below the cost line, meaning the person is not yet covering costs. The revenue line eventually crosses the cost line at a little more than 4 units.
Since the question asks for the minimum number of livestock feeders that must be sold, we need a whole number of feeders.
The graph shows the intersection occurs between:
4 and 5
So selling 4 feeders is not enough, but selling 5 feeders is enough for revenue to cover the costs.
Therefore, the correct answer is:
C
NEW QUESTION # 42
The spread of two viruses within a single population is modeled using the functions in the graph.
What is a correct conclusion based on the graph?
Answer: B
Explanation:
The graph compares the spread of two viruses over time.
The horizontal axis represents:
" time in months "
The vertical axis represents:
" percent of the population affected "
The graph shows:
Virus A as the solid blue curve.
Virus B as the dashed blue curve.
To determine which statement is correct, compare when each virus reaches the same population percentage.
At 20%, Virus A reaches that level earlier than Virus B. The solid curve is already at 20%before the dashed curve reaches 20%.
However, for higher percentages like 70%and 80%, Virus B reaches those levels before Virus A because the dashed curve becomes steeper and rises above the solid curve after about 50%.
So the correct conclusion is:
" Virus A affects " 20% " of the population before virus B does. "
Therefore, the correct answer is:
# ( " A " )
NEW QUESTION # 43
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