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| Section | Objectives |
|---|---|
| Topic 1: Linear Functions | - Interpret rates of change for linear functions - Interpret inputs and outputs of linear functions |
| Topic 2: Polynomial Functions | - Interpret concavity for polynomial functions - Interpret inputs and outputs for polynomial functions - Interpret rates of change for polynomial functions |
| Topic 3: Exponential Functions | - Interpret rates of change for exponential functions - Interpret inputs and outputs for exponential functions - Interpret concavity for exponential functions |
| Topic 4: Graphical Depictions | - Interpret concavity for situations - Interpret rates of change for situations - Interpret maximum and minimum for situations - Interpret asymptotes for situations - Interpret inputs and outputs for situations |
| Topic 5: Logistic Functions | - Interpret rates of change for logistic functions - Interpret inputs and outputs for logistic functions - Interpret asymptotes for logistic functions |
| Topic 6: Functions and Algebra of Functions | - Derive conclusions based on notation - Derive conclusions based on data - Derive conclusions based on graphs |
| Topic 7: Validity of Models | - Examine utility - Determine validity - Determine fit |
>> Applied-Algebra New Learning Materials <<
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NEW QUESTION # 71
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: B
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 # 72
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: C
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 # 73
A researcher collected data on the traffic frequency on a section of road. The results are shown in the scatterplot. A regression function is graphed with r
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