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| Section | Objectives |
|---|---|
| Graphical Depictions | - Interpret inputs and outputs for situations - Interpret concavity for situations - Interpret maximum and minimum for situations - Interpret asymptotes for situations - Interpret rates of change for situations |
| Logistic Functions | - Interpret rates of change for logistic functions - Interpret asymptotes for logistic functions - Interpret inputs and outputs for logistic functions |
| Polynomial Functions | - Interpret rates of change for polynomial functions - Interpret inputs and outputs for polynomial functions - Interpret concavity for polynomial functions |
| Exponential Functions | - Interpret rates of change for exponential functions - Interpret concavity for exponential functions - Interpret inputs and outputs for exponential functions |
| Linear Functions | - Interpret rates of change for linear functions - Interpret inputs and outputs of linear functions |
| Validity of Models | - Determine validity - Determine fit - Examine utility |
| Functions and Algebra of Functions | - Derive conclusions based on data - Derive conclusions based on notation - Derive conclusions based on graphs |
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NEW QUESTION # 20
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: D
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 # 21
The function f(n) represents the relationship between the distances traveled by two vehicles, where n is the distance traveled by vehicle A and f is the distance traveled by vehicle B. The distance traveled by vehicle B is 17 more than the distance traveled by vehicle A.
Which function represents this situation?
Answer: C
Explanation:
The function f(n) gives the distance traveled by vehicle B.
The input n represents the distance traveled by vehicle A.
The problem says vehicle B travels 17 more than vehicle A. The phrase "17 more than" means we add 17 to the amount traveled by vehicle A.
So the relationship is:
f(n)=n+17
For example, if vehicle A traveled 50 miles, then vehicle B traveled:
f(50)=50+17=67
So the correct function is:
f(n)=n+17
Therefore, the correct answer is:
B
NEW QUESTION # 22
The number of acres affected by an invasive species can be modeled using the logistic function f(x), where xrepresents the number of months since the species was introduced and f(x)represents the number of affected acres. The graph of f(x)is shown.
What happens as time progresses from month 2 to month 6?
Answer: C
Explanation:
This is also a logistic growth curve.
Analyze the interval from month 2 to month 6:
The graph is increasing during this time.
The curve is becoming steeper, meaning the slope is increasing.
This indicates the rate of change is getting larger over time.
So, the number of affected acres is:
" increasing faster and faster "
This corresponds to the early-to-middle growth phase of a logistic function.
NEW QUESTION # 23
The populations, in thousands, of two towns are shown in the graph, where the horizontal axis measures the time in years.
Which town's population is growing at a faster rate?
Answer: C
Explanation:
To determine which town's population is growing faster, compare the slopes of the two lines. In a linear population model, the slope represents the growth rate, while the starting value represents the initial population. The graph shows that Town A and Town B both increase over time, but Town B has the larger slope. Town B grows at about 1.3 thousand people per year, while Town A grows at about 1.1 thousand people per year. Since 1.3 > 1.1, Town B's population is increasing at a faster rate. The values 6.5 and 5.5 describe starting population amounts, not growth rates. Therefore, the correct answer is A.
NEW QUESTION # 24
The scatterplot shows data on the population of rabbits in a nature preserve. The graphed regression function has an r
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