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| Section | Objectives |
|---|---|
| Functions and Algebra of Functions | - Derive conclusions based on graphs - Derive conclusions based on data - Derive conclusions based on notation |
| Graphical Depictions | - Interpret asymptotes for situations - Interpret maximum and minimum for situations - Interpret rates of change for situations - Interpret inputs and outputs for situations - Interpret concavity for situations |
| Polynomial Functions | - Interpret rates of change for polynomial functions - Interpret concavity for polynomial functions - Interpret inputs and outputs for polynomial functions |
| Exponential Functions | - Interpret concavity for exponential functions - Interpret inputs and outputs for exponential functions - Interpret rates of change for exponential functions |
| Validity of Models | - Examine utility - Determine fit - Determine validity |
| Logistic Functions | - Interpret rates of change for logistic functions - Interpret inputs and outputs for logistic functions - Interpret asymptotes for logistic functions |
| Linear Functions | - Interpret inputs and outputs of linear functions - Interpret rates of change for linear functions |
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NEW QUESTION # 71
The number of people auditioning for a game show is expected to be 4 times the number of people who auditioned last year. The function A(t) can be used to model the situation, where t represents the number of people who auditioned last year and A represents the number of people expected to audition this year.
Which quantity represents the number of people expected to audition this year, given that 330 people auditioned last year?
Answer: B
Explanation:
We are told that the number of people expected to audition this year is 4 times the number of people who auditioned last year.
Let:
t=number of people who auditioned last year
and
A(t)=number of people expected to audition this year
Since this year's number is 4 times last year's number, the function is:
A(t)=4t
The question says that 330 people auditioned last year, so:
t=330
Now substitute 330 into the function:
A(330)=4(330)
A(330)=1320
So, the correct function notation is:
A(330)=1,320
This means: when 330 people auditioned last year, 1,320 people are expected to audition this year.
Therefore, the correct answer is:
B
NEW QUESTION # 72
The graph shows functions modeling the spread of two diseases within the same population.
Which conclusion is valid?
Answer: D
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 # 73
The graphed function n(t)represents the number of people, n, at a park thours after 8:00 a.m. The plotted points Aand Bhave coordinates (2#110)and (6#182).
Which statement gives the correct interpretation of the average rate of change of the number of people over the interval from point Ato point B?
Answer: C
Explanation:
The average rate of change measures how much the output changes per one unit of input.
Here:
t= " hours after 8:00 a.m. "
and
n(t)= " number of people at the park "
The two given points are:
A=(2,110)
and
B=(6,182)
This means:
At t=2hours after 8:00 a.m., there were 110people at the park.
At t=6hours after 8:00 a.m., there were 182people at the park.
Now calculate the average rate of change:
" Average rate of change " =(182-110)/(6-2)
=72/4
=18
Because the value is positive, the number of people is increasing.
So the correct interpretation is:
" The number of people at the park increases at an average rate of 18 people per hour. "
NEW QUESTION # 74
The graph shows the number of user accounts on a social media website over time.
When did the number of user accounts reach 4,500?
Answer: C
Explanation:
The graph represents the number of user accounts over time.
The horizontal axis represents:
" Time in months "
The vertical axis represents:
" Number of user accounts "
We need to find when the number of user accounts reached:
4,500
On the vertical axis, 4,500is halfway between:
3,000
and
6,000
So we look for the point where the blue curve reaches that height.
From the graph, the curve reaches approximately 4,500user accounts at:
x#2.0
That means the website had about 4,500user accounts after approximately:
2.0 " months "
NEW QUESTION # 75
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:
The average rate of change tells us how much the output changes, on average, for each 1-unit increase in the input.
Here:
x= " hours after 7:00 a.m. "
and
y= " estimated wait time in minutes "
From the graph, point Ais approximately:
A=(5,88.3)
and point Bis approximately:
B=(9,65)
Now use the average rate of change formula:
" Average rate of change " =(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
The negative sign means the estimated wait time is decreasing from point Ato point B.
So the average rate of change is approximately:
-5.83 " minutes per hour "
NEW QUESTION # 76
......
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