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| Section | Objectives |
|---|---|
| Topic 1: Logistic Functions | - Interpret rates of change for logistic functions - Interpret inputs and outputs for logistic functions - Interpret asymptotes for logistic functions |
| Topic 2: Graphical Depictions | - Interpret concavity for situations - Interpret maximum and minimum for situations - Interpret rates of change for situations - Interpret asymptotes for situations - Interpret inputs and outputs for situations |
| Topic 3: Polynomial Functions | - Interpret inputs and outputs for polynomial functions - Interpret concavity for polynomial functions - Interpret rates of change for polynomial functions |
| Topic 4: Functions and Algebra of Functions | - Derive conclusions based on graphs - Derive conclusions based on data - Derive conclusions based on notation |
| Topic 5: Validity of Models | - Determine validity - Examine utility - Determine fit |
| Topic 6: Linear Functions | - Interpret inputs and outputs of linear functions - Interpret rates of change for linear functions |
| Topic 7: Exponential Functions | - Interpret inputs and outputs for exponential functions - Interpret rates of change for exponential functions - Interpret concavity for exponential functions |
>> Exam Applied-Algebra Collection <<
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NEW QUESTION # 97
The scatterplot shows data on the popularity of a blog post over time. The graphed regression function has an r2value of 0.42.
Is it appropriate to make a prediction for the number of daily blog post views after 12.4 days?
Answer: C
Explanation:
Explanation:The regression model has r2=0.42, which indicates a moderate fit. This means the model captures some of the pattern in the data, but it is not strong enough to support distant predictions. The proposed prediction is for x=12.4 days, which lies beyond the largest observed x-value in the scatterplot. Since the model is only moderate, acceptable extrapolation must remain close to the original data range. The value x=12.4 is more than 25% of the range beyond the maximum observed value, so it is too far outside the data for a reliable prediction. Therefore, the prediction is not appropriate. The correct answer is B.
NEW QUESTION # 98
In the following graph showing the elevation profile, F(d), for a mountain biking course, the horizontal axis shows the number of miles since the start of the course and the vertical axis shows the elevation in feet.
How can the concavity be described from d=10 to d=13.1?
Answer: D
Explanation:
This question asks for a description of concavity and rate of change on a specific interval. From d=10 to part of the interval, the elevation is increasing, but the graph becomes less steep as it approaches a local maximum.
That means the elevation increases slower and slower. After the peak, the graph begins to decrease, and the downward slope becomes steeper. This means the elevation decreases faster and faster. The correct statement must describe both parts of the interval in order: first increasing at a slowing rate, then decreasing at an increasing rate. The other answer choices either reverse the behavior or describe the wrong direction of change. Therefore, the correct answer is A.
NEW QUESTION # 99
A researcher collected data on the number of books donated per month to a thrift store over time. The results are shown in the scatterplot. A regression function is graphed with r
2
=0.99.
Which range of x-values is appropriate for extrapolation?
Answer: C
Explanation:
The value r
2
=0.99 indicates a very strong regression fit because it is close to 1. A strong fit means the model explains most of the variation in the data, so limited extrapolation can be appropriate. However, extrapolation should stay close to the observed data range. From the scatterplot, the data values appear to run from about x=5 to x=15. A reasonable extrapolation range extends slightly beyond those observed values, not too far outside them. The interval x=2.5 to x=17.5 stays close to the original data and is more appropriate than the wider interval x=0 to x=20. Therefore, the correct answer is B.
NEW QUESTION # 100
The graph shows the progress of a manufacturing team, modeling the number of widgets the team is able to produce each day since the team was formed.
How should the average rate of change from day 16 to day 18 be interpreted?
Answer: A
Explanation:
The graph models the number of widgets the manufacturing team can produce each day.
The horizontal axis represents:
" Days "
The vertical axis represents:
" Widgets produced each day "
The two labeled points are:
(16#9.1)
and
(18#12.4)
This means:
On day 16, the team could produce about 9.1widgets per day.
On day 18, the team could produce about 12.4widgets per day.
The average rate of change is:
(12.4-9.1)/(18-16)
=3.3/2
=1.65
Rounded to the nearest tenth:
1.7
So from day 16 to day 18, the team's production increased by an average of about:
1.7 " widgets each day "
NEW QUESTION # 101
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: B
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 # 102
......
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