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| Section | Objectives |
|---|---|
| Topic 1: Logistic Functions | - Interpret asymptotes for logistic functions - Interpret inputs and outputs for logistic functions - Interpret rates of change for logistic functions |
| Topic 2: Exponential Functions | - Interpret rates of change for exponential functions - Interpret inputs and outputs for exponential functions - Interpret concavity for exponential functions |
| Topic 3: Validity of Models | - Examine utility - Determine fit - Determine validity |
| Topic 4: Linear Functions | - Interpret inputs and outputs of linear functions - Interpret rates of change for linear functions |
| Topic 5: Graphical Depictions | - Interpret concavity for situations - Interpret maximum and minimum for situations - Interpret rates of change for situations - Interpret asymptotes for situations - Interpret inputs and outputs for situations |
| Topic 6: Polynomial Functions | - Interpret concavity for polynomial functions - Interpret inputs and outputs for polynomial functions - Interpret rates of change for polynomial functions |
| Topic 7: Functions and Algebra of Functions | - Derive conclusions based on graphs - Derive conclusions based on data - Derive conclusions based on notation |
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NEW QUESTION # 124
As sacks are unloaded off a wagon, the total weight of the wagon and sacks changes. Each sack has the same weight. After 3 sacks are removed, the total weight of the cart and remaining sacks is 116 pounds. After 6 sacks are removed, the total weight is 101 pounds.
What is the weight of each sack?
Answer: D
Explanation:
This situation can be modeled using a linear relationship because each sack has the same weight.
We are given:
After 3sacks are removed, the total weight is 116pounds.
After 6sacks are removed, the total weight is 101pounds.
From 3 sacks removed to 6 sacks removed, the number of removed sacks increases by:
6-3=3
During that time, the total weight decreases from 116pounds to 101pounds:
116-101=15
So removing 3 additional sacks decreases the total weight by 15 pounds.
Now divide to find the weight of one sack:
15/3=5
So each sack weighs:
5 " pounds "
Check:
If 3 more sacks are removed and each sack weighs 5 pounds, the total weight should decrease by:
3(5)=15
116-15=101
This matches the given information.
NEW QUESTION # 125
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: A
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 # 126
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: A
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 # 127
The function P(t)represents the weekly profit, in thousands of dollars, for a rental store since opening. The graph of P(t)is shown.
When did the store have its maximum weekly profit?
Answer: B
Explanation:
The graph shows:
P(t)= " weekly profit in thousands of dollars "
where:
t= " years since opening "
The graph is a downward-opening curve, so it has a maximum value at its highest point. In Applied Algebra, the highest point of this kind of polynomial graph is called the vertex.
To answer the question, we need the t-value of the vertex because the question asks when the store had its maximum weekly profit.
From the graph, the highest point occurs between:
t=5
and
t=6
More specifically, it is approximately:
t=5.5
So the store had its maximum weekly profit approximately:
5.5 " years after opening "
NEW QUESTION # 128
The population of fish in a lake is changing according to the function
P(t)=462-35t
where tis the number of months since the beginning of the year and P(t)is the fish population at time t.
Which interpretation of the rate of change is correct?
Answer: A
Explanation:
The function is:
P(t)=462-35t
This is a linear function in the form:
P(t)=mt+b
where:
m= " rate of change "
and
b= " initial value "
In this function:
m=-35
The negative sign means the fish population is decreasing.
The number 35tells us the amount of decrease per month.
So the fish population is decreasing by:
35 " fish per month "
The value 462is not the rate of change. It represents the starting fish population at the beginning of the year, when t=0:
P(0)=462
Therefore, the correct interpretation is:
" The number of fish in the lake is decreasing at a constant rate of 35 fish per month. " So the correct answer is:
# ( " D " )
NEW QUESTION # 129
......
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