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| Section | Objectives |
|---|---|
| Polynomial Functions | - Interpret rates of change for polynomial functions - Interpret concavity for polynomial functions - Interpret inputs and outputs for polynomial functions |
| Linear Functions | - Interpret rates of change for linear functions - Interpret inputs and outputs of linear functions |
| Graphical Depictions | - Interpret asymptotes for situations - Interpret inputs and outputs for situations - Interpret maximum and minimum for situations - Interpret rates of change for situations - Interpret concavity for situations |
| Logistic Functions | - Interpret asymptotes for logistic functions - Interpret rates of change for logistic functions - Interpret inputs and outputs for logistic functions |
| Functions and Algebra of Functions | - Derive conclusions based on data - Derive conclusions based on graphs - Derive conclusions based on notation |
| Exponential Functions | - Interpret inputs and outputs for exponential functions - Interpret rates of change for exponential functions - Interpret concavity for exponential functions |
| Validity of Models | - Determine validity - Determine fit - Examine utility |
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NEW QUESTION # 81
The logistic function f(x), whose graph is shown, models the number of people with a viral infection, where x represents the number of days since the outbreak of the virus and f(x) represents the number of viral infections.
What happens as time progresses from day 9 to day 12?
Answer: C
Explanation:
The graph represents a logistic growth model for viral infections. From day 9 to day 12, the curve is moving upward, so the number of infected people is increasing. During this interval, the graph is also becoming steeper, which means the rate of increase is getting larger. When a function is increasing and its slope is increasing, the correct description is that the quantity increases faster and faster. This interval occurs before the logistic graph begins to level off near its carrying capacity. The choices involving decrease are incorrect because the graph is not going downward. The choice "increases slower and slower" would apply to a later interval where the graph flattens. Therefore, the correct answer is A.
NEW QUESTION # 82
The number of new user accounts per day on a website is modeled by a decreasing exponential function. The graph of the function is shown.
Which statement is justified considering the location of the horizontal asymptote?
Answer: C
Explanation:
The graph shows a decreasing exponential function.
The horizontal axis represents:
" Time in months "
The vertical axis represents:
" New user accounts per day "
The graph starts near 7,000new user accounts per day and decreases over time. However, it does not decrease toward 0. Instead, the graph levels off near a horizontal value around:
y=2,500
This horizontal value is the horizontal asymptote.
A horizontal asymptote shows the long-term value the function approaches. Since the asymptote is above 0, the model predicts that the number of daily new user accounts approaches a positive value, not zero.
So the justified statement is:
" The number of daily new user accounts will not decrease to 0. "
NEW QUESTION # 83
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: C
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 # 84
The graph shows the estimated wait time, in minutes, based on the number of hours after 7:00 a.m.
What is the average rate of change of the wait time from point Ato point B?
Answer: A
Explanation:
From the graph, the horizontal axis represents:
t= " hours after 7:00 a.m. "
The vertical axis represents:
" estimated wait time in minutes "
Point Ais approximately at:
A=(5,88.3)
Point Bis approximately at:
B=(9,65)
The average rate of change from point Ato point Bis calculated using:
(y_2-y_1)/(x_2-x_1 )
Substitute the values:
(65-88.3)/(9-5)
=(-23.3)/4
=-5.825
Rounded to two decimal places:
-5.83
So, the wait time decreases by about:
5.83 " minutes per hour "
NEW QUESTION # 85
The function a(x)represents the value of an investment account, where xis the number of years since the account was opened. The graph of the function is shown.
What is the total value when x=4?
Answer: C
Explanation:
The function a(x)represents the total value of an investment account.
The horizontal axis represents:
x= " time in years "
The vertical axis represents:
a(x)= " total account value in dollars "
We are asked to find the total value when:
x=4
To answer this from the graph:
Locate x=4on the horizontal axis.
Move vertically upward until reaching the blue graph.
Read the corresponding value on the vertical axis.
From the graph, when x=4, the value is slightly above $1,800, approximately:
a(4)#1,830.59
So the total value of the investment account after 4 years is approximately:
$1,830.59
NEW QUESTION # 86
......
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