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| Section | Objectives |
|---|---|
| Topic 1: Validity of Models | - Examine utility - Determine validity - Determine fit |
| Topic 2: Functions and Algebra of Functions | - Derive conclusions based on data - Derive conclusions based on notation - Derive conclusions based on graphs |
| Topic 3: Graphical Depictions | - Interpret inputs and outputs for situations - Interpret asymptotes for situations - Interpret rates of change for situations - Interpret maximum and minimum for situations - Interpret concavity for situations |
| 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: Exponential Functions | - Interpret inputs and outputs for exponential functions - Interpret concavity for exponential functions - Interpret rates of change for exponential functions |
| Topic 6: Polynomial Functions | - Interpret inputs and outputs for polynomial functions - Interpret rates of change for polynomial functions - Interpret concavity for polynomial functions |
| Topic 7: Linear Functions | - Interpret inputs and outputs of linear functions - Interpret rates of change for linear functions |
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NEW QUESTION # 79
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: B
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 # 80
A researcher collected data on the number of books donated per month to a thrift store over time. The results are shown in the scatterplot. A regression function is graphed with r
2
=0.99.
Which range of x-values is appropriate for extrapolation?
Answer: C
Explanation:
The value r
2
=0.99 indicates a very strong regression fit because it is close to 1. A strong fit means the model explains most of the variation in the data, so limited extrapolation can be appropriate. However, extrapolation should stay close to the observed data range. From the scatterplot, the data values appear to run from about x=5 to x=15. A reasonable extrapolation range extends slightly beyond those observed values, not too far outside them. The interval x=2.5 to x=17.5 stays close to the original data and is more appropriate than the wider interval x=0 to x=20. Therefore, the correct answer is B.
NEW QUESTION # 81
The populations, in thousands, of two towns are shown in the graph, where the horizontal axis measures the time in years.
Which town's population is growing at a faster rate?
Answer: B
Explanation:
The graph compares the populations of two towns over time.
The horizontal axis represents:
" Time in years "
The vertical axis represents:
" Population in thousands "
The graph shows:
Town A as the solid blue line.
Town B as the dashed blue line.
To determine which town's population is growing faster, we compare the slopes of the two lines.
In Applied Algebra, the slope of a line represents the rate of change:
" slope " = " change in population " / " change in time "
From the graph:
" Town A grows at about " 0.9 " thousand people per year "
" Town B grows at about " 1.6 " thousand people per year "
Now compare the growth rates:
1.6 > 0.9
So Town B's population is growing at a faster rate.
The values 8.0and 6.5describe starting populations, not growth rates. Since the question asks about growing at a faster rate, we must compare the slopes.
NEW QUESTION # 82
As regulations change, the number of licensed sellers of a product decreases. The graph models the change in the number of licensed sellers over time.
What does the horizontal asymptote mean?
Answer: C
Explanation:
The horizontal asymptote describes the long-term behavior of the function. In this problem, the graph shows a decreasing exponential model for the number of licensed sellers. The graph begins near a higher value and then decreases, eventually leveling off near 300. This means the number of licensed sellers approaches 300 over time. It does not mean the number necessarily becomes exactly 300 at 21 months, and it does not mean the sellers increase back to the initial value. The initial value is separate from the horizontal asymptote. Since the graph levels off around 300, the correct interpretation is that in the long run, the number of licensed sellers nears 300. Therefore, the answer is C.
NEW QUESTION # 83
Which statement correctly interprets u(8), given that u(t)=0.21t
3
#4.09t
2
+18.89t+69.5 represents the number of units, u, in an inventory warehouse t hours after 9:00 a.m.?
Answer: D
Explanation:
The function u(t) gives the number of units in the inventory warehouse t hours after 9:00 a.m. The expression u(8) means the value of the inventory function 8 hours after 9:00 a.m. Since 8 hours after 9:00 a.m. is 5:00 p.
m., the time must be 5:00 p.m., not 10:00 a.m. Now evaluate the function: u(8)=0.21(8)
3
#4.09(8)
2
+18.89(8)+69.5. This gives approximately 66.38, which rounds to about 66 units. Therefore, the correct interpretation is that there are approximately 66 units in the inventory at 5:00 p.m.
NEW QUESTION # 84
......
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