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| Section | Objectives |
|---|---|
| Topic 1: Polynomial Functions | - Interpret inputs and outputs for polynomial functions - Interpret concavity for polynomial functions - Interpret rates of change for polynomial functions |
| Topic 2: Validity of Models | - Determine fit - Examine utility - Determine validity |
| Topic 3: Functions and Algebra of Functions | - Derive conclusions based on graphs - Derive conclusions based on notation - Derive conclusions based on data |
| Topic 4: Logistic Functions | - Interpret asymptotes for logistic functions - Interpret rates of change for logistic functions - Interpret inputs and outputs for logistic functions |
| Topic 5: Graphical Depictions | - Interpret rates of change for situations - Interpret asymptotes for situations - Interpret maximum and minimum for situations - Interpret inputs and outputs for situations - Interpret concavity for situations |
| Topic 6: Exponential Functions | - Interpret concavity for exponential functions - Interpret rates of change for exponential functions - Interpret inputs and outputs for exponential functions |
| Topic 7: Linear Functions | - Interpret rates of change for linear functions - Interpret inputs and outputs of linear functions |
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NEW QUESTION # 117
The populations, in thousands, of two towns are shown in the graph, where the horizontal axis measures the time in years.
Which town's population is growing at a faster rate?
Answer: B
Explanation:
To decide which town is growing faster, compare the slopes of the two lines. In a linear population graph, the slope represents the growth rate, while the starting value represents the initial population. The graph shows that Town A has a slope of about 1.0 thousand people per year, while Town B has a slope of about 0.7 thousand people per year. Since 1.0 > 0.7, Town A is growing at a faster rate. The values 6.5 and 5.5 refer to population amounts, not growth rates, so they do not answer the question. The correct comparison must use the slopes. Therefore, the correct answer is D.
NEW QUESTION # 118
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 # 119
The number of registered voters in a district is modeled by a decreasing exponential function, where x represents the number of years since 2005 and f(x) represents the number of registered voters.
Which interval is associated with the slowest average decrease in the number of registered voters?
Answer: B
Explanation:
A decreasing exponential function falls quickly at first and then levels off over time. The "slowest average decrease" occurs where the graph is flattest, because the output changes by the smallest amount per year.
Earlier intervals, such as 2005 to 2008, occur when the graph is steepest, so those intervals have a faster average decrease. Later intervals occur after the exponential decay has slowed. From the graph, the interval from 2015 to 2025 is farthest to the right and has the least steep downward trend. Therefore, the number of registered voters decreases most slowly during that interval. This is why the correct answer is D.
NEW QUESTION # 120
The graphed function n(t)represents the number of animals, n, at a feeding station thours after 5:00 a.m. The plotted points Aand Bhave coordinates (1#10.6)and (8#6.59).
Which statement gives the correct interpretation of the average rate of change of the number of animals over the interval from point Ato point B?
Answer: B
Explanation:
The average rate of change tells how much the output changes per one unit of input.
Here:
t= " hours after 5:00 a.m. "
and
n(t)= " number of animals "
The two given points are:
A=(1,10.6)
and
B=(8,6.59)
Use the average rate of change formula:
(y_2-y_1)/(x_2-x_1 )
Substitute the coordinates:
(6.59-10.6)/(8-1)
=(-4.01)/7
#-0.573
The negative sign means the number of animals is decreasing.
So the correct interpretation is:
" The number of animals at the station decreases at an average rate of " 0.573 " animals per hour. " Therefore, the correct answer is:
# ( " B " )
NEW QUESTION # 121
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: D
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 # 122
......
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