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| Section | Objectives |
|---|---|
| Topic 1: Linear Functions | - Interpret inputs and outputs of linear functions - Interpret rates of change for linear functions |
| Topic 2: Validity of Models | - Determine validity - Examine utility - Determine fit |
| Topic 3: Exponential Functions | - Interpret inputs and outputs for exponential functions - Interpret rates of change for exponential functions - Interpret concavity for exponential functions |
| Topic 4: Logistic Functions | - Interpret rates of change for logistic functions - Interpret inputs and outputs for logistic functions - Interpret asymptotes for logistic functions |
| Topic 5: Functions and Algebra of Functions | - Derive conclusions based on data - Derive conclusions based on notation - Derive conclusions based on graphs |
| Topic 6: Graphical Depictions | - Interpret asymptotes for situations - Interpret rates of change for situations - Interpret concavity for situations - Interpret maximum and minimum for situations - Interpret inputs and outputs for situations |
| Topic 7: Polynomial Functions | - Interpret inputs and outputs for polynomial functions - Interpret rates of change for polynomial functions - Interpret concavity for polynomial functions |
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NEW QUESTION # 62
The data in the scatterplot represents the number of monthly train crossings at a particular intersection over time.
Which type of function should be used to model the data?
Answer: D
Explanation:
The scatterplot shows the number of monthly train crossings decreasing over time. The decrease is not constant from one year to the next, so a linear model is not the best choice. Instead, the data decreases quickly at first and then begins to level off, which is characteristic of exponential decay. Exponential models are appropriate when a quantity changes by a repeated factor or percentage over equal time intervals. A logistic model would usually show an S-shaped pattern with a carrying capacity, and a polynomial model would be more appropriate for turning points or more complex curvature. Since the points show a smooth decreasing curve that flattens over time, an exponential function best models the data. Therefore, the correct answer is B.
NEW QUESTION # 63
A small business is tracking the number of client accounts it manages over time. The graph shows the relationship between time and the number of client accounts the small business manages.
What is the equation of the horizontal asymptote?
Answer: C
Explanation:
A horizontal asymptote is a horizontal line that a graph approaches as the input increases. Horizontal lines always have equations in the form y=constant, not x=constant. In this graph, the number of client accounts decreases over time and levels off near 125 accounts. Since the graph approaches 125 on the vertical axis, the horizontal asymptote is y=125. Choices x=125 and x=550 are vertical lines, so they cannot represent horizontal asymptotes. Choice y=550 represents a higher value near the beginning of the graph, not the long- term level. Therefore, the correct equation of the horizontal asymptote is y=125, making the answer B.
NEW QUESTION # 64
The weekly number of players, P, in hundreds, on a gaming website is modeled by the graph. The horizontal axis shows the number of years since the website was launched.
When did the website reach the minimum weekly number of players?
Answer: A
Explanation:
The graph shows the weekly number of players on a gaming website.
The horizontal axis represents:
" years since launching "
The vertical axis represents:
" players in hundreds "
The graph is an upward-opening curve, so the minimum value occurs at the lowest point of the graph.
From the graph, the lowest point occurs at approximately:
t=4
This means the website reached its minimum weekly number of players approximately:
4 " years after it was launched "
Therefore, the correct answer is:
# ( " B " )
NEW QUESTION # 65
A factory mixes two colors, red and yellow, to create a dye.
The graph shows the relationship between the amounts of each dye, where rrepresents the amount of red dye and yrepresents the amount of yellow dye.
What is the correct interpretation of the rate of change?
Answer: C
Explanation:
The graph shows a linear relationship between the amount of red dye, r, and the amount of yellow dye, y.
The rate of change of a line is the slope:
" slope " =( " change in " y)/( " change in " r)
From the graph, the line goes through the origin and rises steeply. A clear point on the line is approximately:
(2#9)
This means when the amount of red dye is 2gallons, the amount of yellow dye is 9gallons.
So the rate of change is:
9/2
That means for every 2gallons of red dye, the factory uses 9gallons of yellow dye.
The relationship can be written as:
y=9/2 r
So the correct interpretation is:
" The amount of yellow dye must be " 9/2 " of the amount of red dye. "
Therefore, the correct answer is:
# ( " A " )
NEW QUESTION # 66
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 # 67
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