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| Section | Objectives |
|---|---|
| Validity of Models | - Determine validity - Examine utility - Determine fit |
| Linear Functions | - Interpret rates of change for linear functions - Interpret inputs and outputs of linear functions |
| Functions and Algebra of Functions | - Derive conclusions based on data - Derive conclusions based on notation - Derive conclusions based on graphs |
| Logistic Functions | - Interpret inputs and outputs for logistic functions - Interpret asymptotes for logistic functions - Interpret rates of change for logistic functions |
| Polynomial Functions | - Interpret rates of change for polynomial functions - Interpret inputs and outputs for polynomial functions - Interpret concavity for polynomial functions |
| Exponential Functions | - Interpret rates of change for exponential functions - Interpret inputs and outputs for exponential functions - Interpret concavity for exponential functions |
| Graphical Depictions | - Interpret asymptotes for situations - Interpret rates of change for situations - Interpret inputs and outputs for situations - Interpret maximum and minimum for situations - Interpret concavity for situations |
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NEW QUESTION # 113
A music student attempted to learn a difficult new song. Each day, the student would play the song and be scored on their performance. The graph shows the results.
What was the average daily change in performance from day 16 to day 20?
Answer: A
Explanation:
The average daily change is the average rate of change over the interval from day 16 to day 20. From the graph, the performance score at day 16 is approximately 30.1, and the score at day 20 is approximately 57.6.
Use the formula
x
2
#x
1
y
2
#y
1
Substituting gives
20#16
57.6#30.1
The numerator is 27.5, and the denominator is 4, so the average daily change is 27.5/4=6.875, which rounds to 6.88. This means the performance score increased by an average of about 6.88 points per day over the interval. Therefore, the correct answer is B.
NEW QUESTION # 114
The given function represents the price of a commodity, p, in dollars, based on the number of months, m, since the beginning of 2020.
p(m)=5m+5
What is the average rate of change of the price over the interval m=1to m=10?
Answer: A
Explanation:
The function is:
p(m)=5m+5
This is a linear function in the form:
p(m)=mx+b
For a linear function, the average rate of change over any interval is the same as the slope.
The slope is the coefficient of m:
5
So the price increases at a constant rate of:
$5 " per month "
We can also verify using the average rate of change formula:
(p(10)-p(1))/(10-1)
Find p(10):
p(10)=5(10)+5=55
Find p(1):
p(1)=5(1)+5=10
Now calculate:
(55-10)/(10-1)
=45/9
=5
NEW QUESTION # 115
The graph shows the number of people waiting in a virtual queue to buy tickets for an event.
What does the horizontal asymptote mean?
Answer: D
Explanation:
The graph shows the queue size changing over time.
The horizontal axis represents:
" Time in minutes "
The vertical axis represents:
" Queue size "
The graph is a decreasing exponential curve. It starts near 750people and decreases quickly at first. Then the curve begins to flatten near:
y=100
A horizontal asymptote is the horizontal line that the graph approaches as time continues.
Here, the graph approaches the horizontal line:
y=100
This means that as time passes, the number of people in the virtual queue gets closer and closer to 100.
It does not mean the queue decreases to 0, because the graph levels off near 100, not near 0.
Therefore, the correct interpretation is:
" As time passes, the number of people in the queue approaches 100. "
NEW QUESTION # 116
The graph shows the estimated wait time, in minutes, based on the number of hours after 7:00 a.m.
What is the average rate of change of the wait time from point Ato point B?
Answer: D
NEW QUESTION # 117
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: A
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 # 118
......
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