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| Section | Objectives |
|---|---|
| Topic 1: Exponential and Logarithmic Concepts | - Exponential Functions
|
| Topic 2: Foundations of Algebra | - Equations and Inequalities
|
| Topic 3: Functions and Graphs | - Graphing Functions
|
| Topic 4: Polynomial and Rational Expressions | - Polynomials
|
| Topic 5: Linear Functions and Systems | - Systems of Equations
|
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NEW QUESTION # 43
A researcher collected data on the average selling price for tickets to a concert over time. The results are shown in the scatterplot. A regression function is graphed with r
2=0.56. The predicted average selling price for tickets after 10.8 days is $167.20.
Is this prediction appropriate?
Answer: A
Explanation:
The regression model has r2=0.56, which indicates a moderate fit. A moderate fit is not as reliable as a strong fit, but it can still be used for limited prediction when the extrapolation is close to the observed data. The prediction is made at x=10.8 days. This value is slightly beyond the maximum observed x-value, so the prediction is an extrapolation. For a moderate fit, the x-value should remain within about 25% of the range beyond the maximum value. In this case, x=10.8 is within that acceptable range, so the prediction is appropriate. Therefore, the correct answer is B.
NEW QUESTION # 44
A new company just launched and is using the function M(t) to predict its market share after t years. The graph of M(t) is shown.
When should the company expect to have a market share of 60%?
Answer: C
Explanation:
This question uses a logistic function, which often models growth that starts slowly, increases rapidly, and then levels off near a maximum value. The input t represents years, and M(t) represents market share as a percent. To find when the company reaches a 60% market share, locate 60 on the vertical axis and identify where the graph reaches that height. Then read the corresponding value on the horizontal axis. From the graph, the curve reaches 60% slightly after 6 years, approximately at t=6.6. The value after 6 years is close but not yet at 60%. Therefore, the company should expect to reach 60% market share after about 6.6 years.
The correct answer is D.
NEW QUESTION # 45
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 # 46
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: B
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 # 47
Based on collected data, the number of employees at a firm can be modeled using the function f(x)=10× # 1.09 #
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