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| Section | Objectives |
|---|---|
| Functions and Graphs | - Function Concepts
|
| Polynomial and Rational Expressions | - Polynomials
|
| Linear Functions and Systems | - Systems of Equations
|
| Exponential and Logarithmic Concepts | - Logarithmic Basics
|
| Foundations of Algebra | - Algebraic Expressions
|
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NEW QUESTION # 80
The number of members of a religious organization can be modeled using the logistic function f(x), where xrepresents the number of years since the organization was started and f(x)represents the number of members.
The graph of f(x)is shown.
What is one range of values for which the graph is concave down?
Answer: D
Explanation:
The graph is a logistic growth curve.
A logistic growth curve has two main concavity regions:
" concave up before the inflection point "
and
" concave down after the inflection point "
From the graph, the function increases faster and faster until about:
x=6
After x=6, the graph continues increasing, but it begins to flatten out. That means the number of members is increasing slower and slower.
This is concave down behavior.
Therefore, one interval where the graph is concave down is:
(6#11)
So the correct answer is:
# ( " D " )
NEW QUESTION # 81
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: B
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 # 82
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 # 83
The population of bison in a preserve can be modeled using the logistic function f(x), where x represents the number of years since the preserve was established and f(x) represents the population. The graph of f(x) is shown.
How does the bison population change as time progresses from year 7 to year 10?
Answer: B
Explanation:
A logistic function often increases quickly in the middle and then begins to level off as it approaches a maximum carrying capacity. From year 7 to year 10, the graph is still increasing, so the bison population is going up. However, the curve is becoming flatter during this interval. A flatter curve means the slope is getting smaller, so the population is increasing at a slower rate. This behavior is described as "increases slower and slower." It is not decreasing, because the graph continues to move upward. It is also not increasing faster and faster, because the slope is not becoming steeper in this interval. Therefore, the correct interpretation is answer B.
NEW QUESTION # 84
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 # 85
......
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