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| Section | Objectives |
|---|---|
| Logistic Functions | - Interpret rates of change for logistic functions - Interpret inputs and outputs for logistic functions - Interpret asymptotes for logistic functions |
| Polynomial Functions | - Interpret inputs and outputs for polynomial functions - Interpret concavity for polynomial functions - Interpret rates of change for polynomial functions |
| Exponential Functions | - Interpret concavity for exponential functions - Interpret inputs and outputs for exponential functions - Interpret rates of change for exponential functions |
| Linear Functions | - Interpret inputs and outputs of linear functions - Interpret rates of change for linear functions |
| Validity of Models | - Examine utility - Determine fit - Determine validity |
| Graphical Depictions | - Interpret inputs and outputs for situations - Interpret rates of change for situations - Interpret concavity for situations - Interpret asymptotes for situations - Interpret maximum and minimum for situations |
| Functions and Algebra of Functions | - Derive conclusions based on notation - Derive conclusions based on graphs - Derive conclusions based on data |
>> Applied-Algebra New Real Test <<
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NEW QUESTION # 107
The function V(t)represents the number of travelers, V, in a travel depot thours after 7:00 a.m. The graph of V (t)is shown.
What does V(2)represent?
Answer: C
Explanation:
The function V(t)represents the number of travelers in the travel depot.
The input trepresents:
" hours after 7:00 a.m. "
The output V(t)represents:
" number of travelers "
So V(2)means the number of travelers in the depot:
2 " hours after 7:00 a.m. "
From the graph, when:
t=2
the value of V(t)is approximately:
79.2
Since V(t)measures travelers, not hours, V(2)represents:
79.2 " travelers "
Therefore, the correct answer is:
# ( " D " )
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. The graphed regression function has an r
2value of 0.41. The predicted number of annual bear sightings after 19.4 years is 88.5.
Is this prediction appropriate?
Answer: A
Explanation:
The r2value of 0.41 indicates a moderate fit, not a strong fit. A moderate regression model may sometimes support limited extrapolation, but only if the prediction stays close to the observed data. Here, the prediction is made at x=19.4, which is beyond the maximum x-value shown in the scatterplot. For a moderate fit, extrapolation should be more conservative than for a strong fit. The value x=19.4 is more than 25% of the data range beyond the maximum observed value, so the prediction is too far outside the data. Because the fit is only moderate and the extrapolation distance is too large, the prediction is not appropriate. Therefore, the answer is B.
NEW QUESTION # 109
The number of letters processed daily at a mail center is modeled by the decreasing exponential function shown in the graph.
What is the long-term trend in the number of letters processed per day, based on the equation of the horizontal asymptote?
Answer: B
Explanation:
The graph shows a decreasing exponential function.
In Applied Algebra, a decreasing exponential function may approach a fixed value over time. This fixed value is called the horizontal asymptote.
The horizontal asymptote represents the long-term value that the function gets closer and closer to, but does not necessarily cross or reach exactly.
From the graph, the curve decreases quickly at first, then begins to level off near:
y=1,000
This means that as time continues, the number of letters processed per day approaches:
1,000
So the long-term trend is that the mail center will process about:
1,000 " letters per day "
NEW QUESTION # 110
A new company just launched and is using the function M(t)to predict its market share after tyears. The graph of M(t)is shown.
When should the company expect to have a market share of 60%?
Answer: B
Explanation:
The function M(t)represents the company's predicted market share after tyears.
The horizontal axis represents:
t= " time in years "
The vertical axis represents:
M(t)= " market share percentage "
We need to find when the company's market share reaches:
60%
To answer this from the graph:
Locate 60on the vertical axis.
Move horizontally until reaching the blue curve.
Move downward to the horizontal axis to read the corresponding time.
From the graph, the blue curve reaches 60%a little after 6years, approximately at:
t=6.6
So the company should expect to have a market share of 60%after about:
6.6 " years "
NEW QUESTION # 111
A researcher collected data on the number of large donations per year to a charitable organization. The results are shown in the scatterplot. A regression function is graphed with r
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