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| Section | Objectives |
|---|---|
| Logistic Functions | - Interpret inputs and outputs for logistic functions - Interpret asymptotes for logistic functions - Interpret rates of change for logistic functions |
| Validity of Models | - Determine fit - Determine validity - Examine utility |
| Functions and Algebra of Functions | - Derive conclusions based on notation - Derive conclusions based on graphs - Derive conclusions based on data |
| Linear Functions | - Interpret inputs and outputs of linear functions - Interpret rates of change for linear functions |
| Exponential Functions | - Interpret concavity for exponential functions - Interpret inputs and outputs for exponential functions - Interpret rates of change for exponential functions |
| Graphical Depictions | - Interpret inputs and outputs for situations - Interpret asymptotes for situations - Interpret maximum and minimum for situations - Interpret rates of change for situations - Interpret concavity for situations |
| Polynomial Functions | - Interpret inputs and outputs for polynomial functions - Interpret concavity for polynomial functions - Interpret rates of change for polynomial functions |
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NEW QUESTION # 45
A researcher collected data on the average number of product returns per month to a company over time. The results are shown in the scatterplot. The graphed regression function has an r
2
value of 0.45.
Which range of x-values is appropriate for extrapolation?
Answer: C
Explanation:
The coefficient of determination, r
2
, measures how well a regression model fits the data. A value close to 1 indicates a strong fit, while a lower value indicates that the model does not explain the data as reliably. Here, r
2
=0.45, which is below 0.7. That means the model does not have a strong enough fit for reliable extrapolation in this question. Extrapolation means using the model to predict values outside the observed data range, which is riskier than interpolation. Because the model fit is not strong, choosing an extended range of x-values would not be appropriate. The correct reason is that extrapolation is not appropriate because r
2
< 0.7. Therefore, the answer is D.
NEW QUESTION # 46
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: C
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 # 47
After a water tank starts leaking, the amount of water in the tank is modeled by the exponential function that is graphed.
Which statement is justified considering the location of the horizontal asymptote?
Answer: A
Explanation:
The graph shows the water volume decreasing over time.
The vertical axis represents:
" Water volume in gallons "
The horizontal axis represents:
" Time in minutes "
The graph is an exponential decay curve. It decreases quickly at first, then levels off.
From the graph, the curve approaches a horizontal value near:
y=1,000
This means the horizontal asymptote is approximately:
y=1,000
Since the graph approaches 1,000 gallons, it will not decrease to 500 gallons according to this model.
The water volume does not change by a constant rate because exponential functions do not have constant additive change. Also, the graph decreases fastest at the beginning, not later.
NEW QUESTION # 48
Based on collected data, the number of employees at a firm can be modeled using the function f(x)=10× # 1.09 #
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