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| Section | Objectives |
|---|---|
| Exponential Functions | - Interpret inputs and outputs for exponential functions - Interpret concavity for exponential functions - Interpret rates of change for exponential functions |
| Logistic Functions | - Interpret asymptotes for logistic functions - Interpret rates of change for logistic functions - Interpret inputs and outputs for logistic functions |
| Functions and Algebra of Functions | - Derive conclusions based on graphs - Derive conclusions based on data - Derive conclusions based on notation |
| Polynomial Functions | - Interpret rates of change for polynomial functions - Interpret concavity for polynomial functions - Interpret inputs and outputs for polynomial functions |
| Graphical Depictions | - Interpret inputs and outputs for situations - Interpret maximum and minimum for situations - Interpret concavity for situations - Interpret asymptotes for situations - Interpret rates of change for situations |
| Linear Functions | - Interpret inputs and outputs of linear functions - Interpret rates of change for linear functions |
| Validity of Models | - Determine validity - Examine utility - Determine fit |
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NEW QUESTION # 47
As a drone travels away from an operator, the function G(x)=24+47x models the distance, in yards, between the drone and the operator at x minutes. What is the value of G(1.9)?
Answer: B
Explanation:
This is a linear function evaluation problem. The function G(x)=24+47x gives the drone's distance from the operator after x minutes. The constant 24 is the starting distance, and 47 is the rate of change in yards per minute. To evaluate G(1.9), substitute 1.9 for x. Then compute G(1.9)=24+47(1.9). Multiplying first gives
47×1.9=89.3. Adding 24 gives 113.3. Because the function measures distance in yards, the result means the drone is 113.3 yards from the operator after 1.9 minutes. The other options do not result from correctly substituting 1.9 into the function. Therefore, the correct answer is D.
NEW QUESTION # 48
The population of bison in a preserve can be modeled using the logistic function f(x), where x represents the number of years since the preserve was established and f(x) represents the population. The graph of f(x) is shown.
How does the bison population change as time progresses from year 7 to year 10?
Answer: C
Explanation:
A logistic function often increases quickly in the middle and then begins to level off as it approaches a maximum carrying capacity. From year 7 to year 10, the graph is still increasing, so the bison population is going up. However, the curve is becoming flatter during this interval. A flatter curve means the slope is getting smaller, so the population is increasing at a slower rate. This behavior is described as "increases slower and slower." It is not decreasing, because the graph continues to move upward. It is also not increasing faster and faster, because the slope is not becoming steeper in this interval. Therefore, the correct interpretation is answer B.
NEW QUESTION # 49
The graph shows the number of customers, C(t), showing up to a store, where the number of hours since opening is along the horizontal axis and the number of customers showing up to the store each hour is along the vertical axis.
How can the concavity be described from t=6.2to t=10.1?
Answer: A
Explanation:
From t=6.2to about t=8.5, the graph is increasing, but it is becoming less steep as it approaches a local maximum.
That means the number of customers is:
" increasing slower and slower "
After the local maximum, from about t=8.5to t=10.1, the graph begins to decrease and becomes steeper downward.
That means the number of customers is:
" decreasing faster and faster "
So the full description is:
" The number of customers increases slower and slower and then decreases faster and faster. " Therefore, the correct answer is:
# ( " D " )
NEW QUESTION # 50
The number of employees under supervisor B is 13 more than the number of employees under supervisor A.
Let F(n)represent the number of employees under the two supervisors, where nis the number of employees under supervisor A and Fis the number of employees under supervisor B.
Which is the correct function to represent this relationship?
Answer: C
Explanation:
We are told that supervisor B has 13 more employees than supervisor A.
Let:
n= " number of employees under supervisor A "
and
F(n)= " number of employees under supervisor B "
The phrase "13 more than" means we add 13:
F(n)=n+13
So, if supervisor A has nemployees, supervisor B has 13 additional employees.
For example, if supervisor A had 20 employees, then supervisor B would have:
F(20)=20+13=33
Therefore, the correct answer is:
# ( " C " )
NEW QUESTION # 51
Consider the graph of h(t) shown. The function represents the height, h, in feet, of a ball t seconds after being launched.
What is the point, if any, at which the concavity changes from concave down to concave up?
Answer: C
Explanation:
The graph represents the height of a launched ball over time. Such height functions are typically quadratic because gravity causes the ball to rise, slow down, reach a maximum height, and then fall. The graph shown is a downward-opening parabola. A downward-opening parabola is concave down for its entire domain.
Concavity changes only if the curve switches from bending downward to bending upward, or from bending upward to bending downward. Since this graph bends downward the entire time, there is no point where the concavity changes from concave down to concave up. The vertex is a maximum point, but it is not a change in concavity. Therefore, the correct statement is that the graph is always concave down.
NEW QUESTION # 52
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