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| Section | Objectives |
|---|---|
| Topic 1: Polynomial Functions | - Interpret concavity for polynomial functions - Interpret inputs and outputs for polynomial functions - Interpret rates of change for polynomial functions |
| Topic 2: Validity of Models | - Examine utility - Determine fit - Determine validity |
| Topic 3: Linear Functions | - Interpret rates of change for linear functions - Interpret inputs and outputs of linear functions |
| Topic 4: Functions and Algebra of Functions | - Derive conclusions based on graphs - Derive conclusions based on notation - Derive conclusions based on data |
| Topic 5: Exponential Functions | - Interpret inputs and outputs for exponential functions - Interpret rates of change for exponential functions - Interpret concavity for exponential functions |
| Topic 6: Graphical Depictions | - Interpret asymptotes for situations - Interpret concavity for situations - Interpret maximum and minimum for situations - Interpret inputs and outputs for situations - Interpret rates of change for situations |
| Topic 7: Logistic Functions | - Interpret rates of change for logistic functions - Interpret asymptotes for logistic functions - Interpret inputs and outputs for logistic functions |
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NEW QUESTION # 71
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: B
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 # 72
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: C
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 # 73
The number of wild horses in a federal park is represented by the logistic function f(x), whose graph is shown, where xrepresents the number of years since the park was established and f(x)represents the wild horse population in a given year.
How does the number of wild horses change as time progresses from year 1 to year 9?
Answer: A
Explanation:
The graph is a logistic growth function.
A logistic function often has an S-shape. It begins by increasing slowly, then increases faster and faster, and later levels off as it approaches a maximum carrying capacity.
From year 1 to year 9, the graph is rising and becoming steeper.
That means:
" the wild horse population is increasing "
and the slope is getting larger, so:
" the population is increasing faster and faster "
Therefore, the correct answer is:
# ( " A " )
NEW QUESTION # 74
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: C
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 # 75
An investment account accrues interest every year, and the value of the account is given by G(x). The graph of this function is shown.
What represents the value of the account after 4 years?
Answer: D
Explanation:
The graph represents the value of an investment account over time. The horizontal axis gives time in years, and the vertical axis gives the total account value in dollars. To find the value after 4 years, locate x=4 on the horizontal axis and read the corresponding G(x)-value on the graph. The plotted exponential growth curve is slightly above $1,000 at 4 years, closest to $1,052.87. Because the graph shows an increasing exponential trend, values such as $480.52, $584.62, and $711.28 are too low for the account value at x=4. The correct interpretation is that after 4 years, the investment account is worth approximately $1,052.87. Therefore, the correct answer is D.
NEW QUESTION # 76
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