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| Section | Objectives |
|---|---|
| Exponential Functions | - Interpret concavity for exponential functions - Interpret inputs and outputs for exponential functions - Interpret rates of change for exponential functions |
| Functions and Algebra of Functions | - Derive conclusions based on notation - Derive conclusions based on data - Derive conclusions based on graphs |
| Linear Functions | - Interpret rates of change for linear functions - Interpret inputs and outputs of linear functions |
| Graphical Depictions | - Interpret maximum and minimum for situations - Interpret inputs and outputs for situations - Interpret rates of change for situations - Interpret concavity for situations - Interpret asymptotes for situations |
| Polynomial Functions | - Interpret inputs and outputs for polynomial functions - Interpret concavity for polynomial functions - Interpret rates of change for polynomial functions |
| Logistic Functions | - Interpret inputs and outputs for logistic functions - Interpret rates of change for logistic functions - Interpret asymptotes for logistic functions |
| Validity of Models | - Determine fit - Determine validity - Examine utility |
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NEW QUESTION # 113
The figure shows the graph of p(t), which represents the number of people, p, at a gym thours after 7:00 a.m.
How should the concavity between t=1.3and t=3.4be interpreted?
Answer: B
Explanation:
The graph represents:
p(t)= " number of people at the gym "
where:
t= " hours after 7:00 a.m. "
The question asks about the concavity of the graph between:
t=1.3
and
t=3.4
On this interval, the graph is still going upward, so the number of people is increasing.
However, the graph is beginning to flatten as it approaches its highest point. That means the slope is positive, but the slope is getting smaller.
In other words:
" The number of people is increasing, but at a slower rate. "
This is called concave down behavior. For a concave down graph that is increasing, the correct interpretation is:
" increasing slower and slower "
Therefore, the correct answer is:
# ( " C " )
NEW QUESTION # 114
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 # 115
A company provides internet service to approximately 1,050 customers each year. The table shows the percentage of customers with fiber internet each year since 2020.
Years since 2020 Percent of Customers with Fiber
0 19
1 28
2 40
3 57
What was the approximate number of customers with fiber internet in 2023?
Answer: A
Explanation:
The table gives the percent of customers with fiber internet for each year since 2020.
Since 2023 is:
2023#2020=3
we use the row where:
Years since 2020=3
From the table, the percent of customers with fiber internet in 2023 is:
57%
The company has approximately:
1,050
customers each year.
Now find 57% of 1,050:
0.57×1,050=598.5
The closest answer choice is:
598
So approximately 598 customers had fiber internet in 2023.
Therefore, the correct answer is:
C
NEW QUESTION # 116
The spread of two viruses within a single population is modeled using the functions in the graph.
What is a correct conclusion based on the graph?
Answer: C
Explanation:
The graph compares the spread of two viruses over time.
The horizontal axis represents:
" time in months "
The vertical axis represents:
" percent of the population affected "
The graph shows:
Virus A as the solid blue curve.
Virus B as the dashed blue curve.
To determine which statement is correct, compare when each virus reaches the same population percentage.
At 20%, Virus A reaches that level earlier than Virus B. The solid curve is already at 20%before the dashed curve reaches 20%.
However, for higher percentages like 70%and 80%, Virus B reaches those levels before Virus A because the dashed curve becomes steeper and rises above the solid curve after about 50%.
So the correct conclusion is:
" Virus A affects " 20% " of the population before virus B does. "
Therefore, the correct answer is:
# ( " A " )
NEW QUESTION # 117
The number of comments on a social media post is represented by the logistic function f(x), whose graph is shown, where xrepresents the number of days since the post was created and f(x)represents the number of comments on day x.
How does the number of comments change as time progresses from day 1 to day 17?
Answer: C
Explanation:
This graph represents a logistic growth function, which has an S-shaped curve.
Key behavior of logistic functions:
Initial phase (early time) # growth is slow
Middle phase # growth speeds up (increasing rate)
Later phase # growth slows down as it approaches a maximum
Analyze the interval from day 1 to day 17:
This interval is in the early part of the graph.
The curve is increasing and getting steeper over this range.
That means the rate of increase is growing over time.
So, the number of comments is:
" increasing faster and faster "
NEW QUESTION # 118
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