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| Section | Objectives |
|---|---|
| Exponential Functions | - Interpret concavity for exponential functions - Interpret rates of change for exponential functions - Interpret inputs and outputs for exponential functions |
| Linear Functions | - Interpret rates of change for linear functions - Interpret inputs and outputs of linear functions |
| Functions and Algebra of Functions | - Derive conclusions based on notation - Derive conclusions based on graphs - Derive conclusions based on data |
| Graphical Depictions | - Interpret concavity for situations - Interpret asymptotes for situations - Interpret maximum and minimum for situations - Interpret inputs and outputs for situations - Interpret rates of change for situations |
| Logistic Functions | - Interpret asymptotes for logistic functions - Interpret rates of change for logistic functions - Interpret inputs and outputs for logistic functions |
| Polynomial Functions | - Interpret concavity for polynomial functions - Interpret rates of change for polynomial functions - Interpret inputs and outputs for polynomial functions |
| Validity of Models | - Determine fit - Determine validity - Examine utility |
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NEW QUESTION # 97
A coach is placing an order for team shirts. The graph shows the total cost based on the number of shirts.
What is the cost of each additional shirt?
Exhibit:
Answer: B
Explanation:
This question asks for the cost of each additional shirt, which is the slope of the linear graph. The slope tells how much the total cost increases for each increase of 1 shirt. From the exhibit, the graph shows a starting cost near $39 and a point near (10, 139). The increase in cost from 0 shirts to 10 shirts is 139#39=100 dollars.
Dividing by 10 shirts gives a rate of 10 dollars per shirt. The fixed starting cost is not the cost of a shirt; it is the initial fee or setup cost. Since the graph rises by $10 for each additional shirt, the cost per additional shirt is $10.00. Therefore, the answer is B.
NEW QUESTION # 98
The graph shows the total cost of a lumber delivery based on the number of identical boards ordered.
What is the cost of each additional board?
Answer: B
Explanation:
The graph shows a linear relationship between:
" Number of boards "
and
" Total cost "
The cost of each additional board is the rate of change, or slope, of the line.
From the graph, two labeled points are:
(0#27)
and
(10#177)
This means:
When 0 boards are ordered, the total cost is $27.
When 10 boards are ordered, the total cost is $177.
Now calculate the slope:
m=(177-27)/(10-0)
m=150/10
m=15
So each additional board costs:
$15
Therefore, the correct answer is:
# ( " B " )
NEW QUESTION # 99
The function P(t)represents the daily profit, in hundreds of dollars, for a museum since opening. The graph of P(t)is shown.
What is the correct interpretation of the maximum value?
Answer: B
Explanation:
The graph shows a curved, downward-opening function. This type of graph is commonly associated with a quadratic polynomial function.
The maximum value of a downward-opening parabola occurs at its highest point, called the vertex.
From the graph, the highest point occurs at approximately:
t=9.5
This means the museum reaches its maximum daily profit approximately:
9.5 " years after opening "
The vertical axis represents daily profit in hundreds of dollars. From the graph, the maximum P(t)-value is approximately:
16.5
Since the profit is measured in hundreds of dollars:
16.5×100=1650
So the maximum daily profit is approximately:
$1,650
Therefore, the correct interpretation is:
" Approximately 9.5 years after opening, a maximum daily profit of approximately " $1,650 " was earned. "
NEW QUESTION # 100
Based on collected data, the value of a painting can be modeled using the exponential function f(x)=240(1.12) x
. In this case, x represents the number of years since 2005, and f(x) represents the value of the painting in dollars.
Which value represents the average yearly rate of change of the painting's value from 2013 to 2015?
Answer: A
Explanation:
This problem asks for an average yearly rate of change over a time interval. Since x represents years since
2005, the year 2013 corresponds to x=8, and the year 2015 corresponds to x=10. Use the average rate of change formula:
10#8
f(10)#f(8)
Evaluating the model gives f(8)=240(1.12)
8
#594.23 and f(10)=240(1.12)
10
#745.40. The total change is approximately 151.17 dollars over 2 years. Dividing by 2 gives about 75.59 dollars per year. Since the question asks for the average yearly rate, not the total increase, the correct answer is B.
NEW QUESTION # 101
The weekly number of players, P, in hundreds, on a gaming website is modeled by the graph. The horizontal axis shows the number of years since the website was launched.
When did the website reach the minimum weekly number of players?
Answer: D
Explanation:
The graph shows the weekly number of players on a gaming website.
The horizontal axis represents:
" years since launching "
The vertical axis represents:
" players in hundreds "
The graph is an upward-opening curve, so the minimum value occurs at the lowest point of the graph.
From the graph, the lowest point occurs at approximately:
t=4
This means the website reached its minimum weekly number of players approximately:
4 " years after it was launched "
Therefore, the correct answer is:
# ( " B " )
NEW QUESTION # 102
......
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