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| Section | Objectives |
|---|---|
| Logistic Functions | - Interpret inputs and outputs for logistic functions - Interpret rates of change for logistic functions - Interpret asymptotes for logistic functions |
| Polynomial Functions | - Interpret inputs and outputs for polynomial functions - Interpret rates of change for polynomial functions - Interpret concavity for polynomial functions |
| Validity of Models | - Determine fit - Examine utility - Determine validity |
| Linear Functions | - Interpret inputs and outputs of linear functions - Interpret rates of change for linear functions |
| Graphical Depictions | - Interpret asymptotes for situations - Interpret inputs and outputs for situations - Interpret concavity for situations - Interpret rates of change for situations - Interpret maximum and minimum for situations |
| Exponential Functions | - Interpret inputs and outputs for exponential functions - Interpret rates of change for exponential functions - Interpret concavity for exponential functions |
| Functions and Algebra of Functions | - Derive conclusions based on data - Derive conclusions based on graphs - Derive conclusions based on notation |
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NEW QUESTION # 115
The function P(t)represents the yearly profit, in millions of dollars, for a streaming service since opening. The graph of P(t)is shown.
What is the correct interpretation of the maximum value?
Answer: B
Explanation:
The graph represents yearly profit as a function of time:
P(t)= " yearly profit "
where:
t= " years since opening "
The graph is a downward-opening curve, so its maximum value occurs at the highest point, also called the vertex.
From the graph, the highest point occurs at approximately:
t=10.5
So the maximum yearly profit happened approximately:
10.5 " years after opening "
The vertical axis measures yearly profit in millions of dollars. From the graph, the maximum value is approximately:
1.41
Since the units are millions of dollars:
1.41×1,000,000=1,410,000
So the maximum yearly profit was approximately:
$1,410,000
Therefore, the correct answer is:
# ( " C " )
NEW QUESTION # 116
The number of property sales in a region this year is expected to be 6 less than the number of property sales in the region last year. The function H(x)represents the number of property sales this year, where xrepresents the number of properties sold last year.
Which notation represents the number of property sales this year, given that the number of properties sold last year was 330?
Answer: C
Explanation:
We are told that this year's number of property sales is 6 less than last year's number of property sales.
Let:
x= " number of properties sold last year "
and
H(x)= " number of property sales this year "
Since this year's sales are 6 less than last year's sales, the function rule is:
H(x)=x-6
The question says that the number of properties sold last year was:
x=330
Substitute 330into the function:
H(330)=330-6
H(330)=324
So the notation that correctly represents the number of property sales this year is:
H(330)=324
This means: if 330 properties were sold last year, then 324 properties are expected to be sold this year.
NEW QUESTION # 117
A new company just launched and is using the function M(t)to predict its market share after tyears. The graph of M(t)is shown.
When should the company expect to have a market share of 40%?
Answer: A
Explanation:
The function M(t)represents the company's market share after tyears.
The horizontal axis represents:
t= " time in years "
The vertical axis represents:
M(t)= " market share percentage "
We need to find when the market share reaches:
40%
From the graph, locate 40on the vertical axis. Then move horizontally to the blue curve and read the corresponding value on the horizontal axis.
The curve reaches 40%at approximately:
t=7.4
So the company should expect to have a market share of 40%after about:
7.4 " years "
Therefore, the correct answer is:
# ( " C " )
NEW QUESTION # 118
An exponential growth function can be used to model the number of bacteria in a population. The function G(t)=1,600× # 1.31 #
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