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| Section | Objectives |
|---|---|
| Functions and Algebra of Functions | - Derive conclusions based on graphs - Derive conclusions based on data - Derive conclusions based on notation |
| 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 validity - Examine utility - Determine fit |
| Linear Functions | - Interpret rates of change for linear functions - Interpret inputs and outputs of linear functions |
| Graphical Depictions | - Interpret rates of change for situations - Interpret concavity for situations - Interpret inputs and outputs for situations - Interpret maximum and minimum for situations - Interpret asymptotes for situations |
| Polynomial Functions | - Interpret concavity for polynomial functions - Interpret rates of change for polynomial functions - Interpret inputs and outputs for polynomial functions |
| Exponential Functions | - Interpret rates of change for exponential functions - Interpret inputs and outputs for exponential functions - Interpret concavity for exponential functions |
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NEW QUESTION # 67
The function p(t)represents the number of active players, p, in a game thours after 11:00 a.m. The graph of p(t) is shown.
What is one example of an interval for which the number of players is decreasing faster and faster?
Answer: C
Explanation:
The graph represents:
p(t)= " number of active players "
where:
t= " hours after 11:00 a.m. "
The phrase "decreasing faster and faster" means two things are happening:
The graph is going downward, so the number of players is decreasing.
The graph is becoming steeper downward, so the rate of decrease is increasing.
This corresponds to a graph that is decreasing and concave down.
Looking at the graph, the number of active players reaches a maximum around:
t#9
After that, the graph begins decreasing. Near the far right side of the graph, especially around:
t=11.2 " to " t=11.5
the curve is dropping more and more steeply.
That means the number of players is decreasing faster and faster on that interval.
NEW QUESTION # 68
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: D
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 # 69
The function d(x)=14+65xrepresents the distance, in meters, from a tower to an object at time x, in seconds.
What is the value of d(1.5)?
Answer: C
Explanation:
We are given the function:
d(x)=14+65x
This is a linear function because it has the form:
d(x)=mx+b
where 65is the rate of change and 14is the starting value.
We need to find:
d(1.5)
That means substitute x=1.5into the function:
d(1.5)=14+65(1.5)
Now multiply:
65(1.5)=97.5
Then add:
d(1.5)=14+97.5
d(1.5)=111.5
So the distance from the tower to the object at 1.5seconds is:
111.5 " meters "
NEW QUESTION # 70
The graph shows functions modeling the spread of two diseases within the same population.
Which conclusion is valid?
Answer: A
Explanation:
This problem compares two logistic growth curves. Each curve shows the percentage of the population affected by a disease over time. To determine which conclusion is valid, compare when each disease reaches the same percentage level. From the graph, Disease B reaches the 70% population level before Disease A reaches 70%. This means Disease B affects 70% of the population earlier in time. For other listed percentages, the graph does not support the same timing relationship as clearly or correctly. Logistic curves can cross or change relative position, so it is important to compare the same output level on both curves. Based on the graph, the valid conclusion is that Disease B affects 70% of the population before Disease A does. The answer is D.
NEW QUESTION # 71
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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