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| Section | Objectives |
|---|---|
| Linear Functions | - Interpret inputs and outputs of linear functions - Interpret rates of change for linear functions |
| Logistic Functions | - Interpret asymptotes for logistic functions - Interpret inputs and outputs for logistic functions - Interpret rates of change for logistic functions |
| Polynomial Functions | - Interpret inputs and outputs for polynomial functions - Interpret rates of change for polynomial functions - Interpret concavity for polynomial functions |
| Exponential Functions | - Interpret inputs and outputs for exponential functions - Interpret concavity for exponential functions - Interpret rates of change for exponential functions |
| Functions and Algebra of Functions | - Derive conclusions based on graphs - Derive conclusions based on notation - Derive conclusions based on data |
| Validity of Models | - Determine fit - Examine utility - Determine validity |
| Graphical Depictions | - Interpret rates of change for situations - Interpret asymptotes for situations - Interpret maximum and minimum for situations - Interpret concavity for situations - Interpret inputs and outputs for situations |
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NEW QUESTION # 94
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: C
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 # 95
An investment account accrues interest every year, and the value of the account is given by G(x). The graph of this function is shown.
What represents the value of the account after 4 years?
Answer: A
Explanation:
The graph represents the value of an investment account over time. The horizontal axis gives time in years, and the vertical axis gives the total account value in dollars. To find the value after 4 years, locate x=4 on the horizontal axis and read the corresponding G(x)-value on the graph. The plotted exponential growth curve is slightly above $1,000 at 4 years, closest to $1,052.87. Because the graph shows an increasing exponential trend, values such as $480.52, $584.62, and $711.28 are too low for the account value at x=4. The correct interpretation is that after 4 years, the investment account is worth approximately $1,052.87. Therefore, the correct answer is D.
NEW QUESTION # 96
The graph shows the progress of a manufacturing team, modeling the number of widgets the team is able to produce each day since the team was formed.
How should the average rate of change from day 20 to day 26 be interpreted?
Answer: C
Explanation:
The average rate of change compares the change in output to the change in input over an interval. From the graph, the two labeled points are approximately (20,58.5) and (26,91.2). The input is days, and the output is widgets produced each day. Use the formula x
2
#x
1
y
2
#y
1
Substituting gives
26#20
91.2#58.5
=
6
32.7
=5.45, which rounds to approximately 5.5. Since this value is an average rate, it means the team's daily production increased by about 5.5 widgets each day during the interval. It is not the total number of additional widgets over the whole interval. Therefore, the correct answer is A.
NEW QUESTION # 97
The function p(t)represents the number of active players, p, in a game thours after 11:00 a.m. The graph of p(t) is shown.
What is one example of an interval for which the number of players is decreasing faster and faster?
Answer: C
Explanation:
The graph represents:
p(t)= " number of active players "
where:
t= " hours after 11:00 a.m. "
The phrase "decreasing faster and faster" means two things are happening:
The graph is going downward, so the number of players is decreasing.
The graph is becoming steeper downward, so the rate of decrease is increasing.
This corresponds to a graph that is decreasing and concave down.
Looking at the graph, the number of active players reaches a maximum around:
t#9
After that, the graph begins decreasing. Near the far right side of the graph, especially around:
t=11.2 " to " t=11.5
the curve is dropping more and more steeply.
That means the number of players is decreasing faster and faster on that interval.
NEW QUESTION # 98
The growth of an animal population is shown in the graph. The instantaneous rate of change at point Pis 3.74.
Which interpretation of the instantaneous rate of change is correct?
Answer: C
Explanation:
The graph shows population in thousands, and the horizontal axis represents:
" years since 1995 "
Point Pis located at approximately:
x=12
Since xrepresents years since 1995:
1995+12=2007
So point Pcorresponds to the year:
2007
The instantaneous rate of change at point Pis:
3.74
Because the vertical axis is measured in thousands, this means:
3.74 " thousand animals per year "
Convert thousands to actual animals:
3.74×1000=3740
So in 2007, the population was increasing by approximately:
3,740 " animals per year "
NEW QUESTION # 99
......
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