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| Section | Objectives |
|---|---|
| Functions and Algebra of Functions | - Derive conclusions based on data - Derive conclusions based on notation - Derive conclusions based on graphs |
| Exponential Functions | - Interpret rates of change for exponential functions - Interpret inputs and outputs for exponential functions - Interpret concavity for exponential functions |
| Polynomial Functions | - Interpret inputs and outputs for polynomial functions - Interpret rates of change for polynomial functions - Interpret concavity for polynomial functions |
| Graphical Depictions | - Interpret rates of change for situations - Interpret concavity for situations - Interpret inputs and outputs for situations - Interpret asymptotes for situations - Interpret maximum and minimum for situations |
| Linear Functions | - Interpret inputs and outputs of linear functions - Interpret rates of change for linear functions |
| Logistic Functions | - Interpret rates of change for logistic functions - Interpret asymptotes for logistic functions - Interpret inputs and outputs for logistic functions |
| Validity of Models | - Examine utility - Determine fit - Determine validity |
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NEW QUESTION # 71
The logistic function f(x), whose graph is shown, models the number of people with a viral infection, where x represents the number of days since the outbreak of the virus and f(x) represents the number of viral infections.
What happens as time progresses from day 9 to day 12?
Answer: A
Explanation:
The graph represents a logistic growth model for viral infections. From day 9 to day 12, the curve is moving upward, so the number of infected people is increasing. During this interval, the graph is also becoming steeper, which means the rate of increase is getting larger. When a function is increasing and its slope is increasing, the correct description is that the quantity increases faster and faster. This interval occurs before the logistic graph begins to level off near its carrying capacity. The choices involving decrease are incorrect because the graph is not going downward. The choice "increases slower and slower" would apply to a later interval where the graph flattens. Therefore, the correct answer is A.
NEW QUESTION # 72
The number of members of a religious organization can be modeled using the logistic function f(x), where xrepresents the number of years since the organization was started and f(x)represents the number of members.
The graph of f(x)is shown.
What is one range of values for which the graph is concave down?
Answer: A
Explanation:
The graph is a logistic growth curve.
A logistic growth curve has two main concavity regions:
" concave up before the inflection point "
and
" concave down after the inflection point "
From the graph, the function increases faster and faster until about:
x=6
After x=6, the graph continues increasing, but it begins to flatten out. That means the number of members is increasing slower and slower.
This is concave down behavior.
Therefore, one interval where the graph is concave down is:
(6#11)
So the correct answer is:
# ( " D " )
NEW QUESTION # 73
A vehicle is traveling away from a town at a fixed rate. After 1 hours, the vehicle is 200 miles from the town.
After 4 hours, the vehicle is 395 miles from the town.
Which function represents the distance, d, between the vehicle and the town after thours?
Answer: A
Explanation:
Because the vehicle is traveling away from the town at a fixed rate, the distance can be modeled by a linear function:
d(t)=mt+b
where:
m= " rate of change "
and
b= " initial distance from the town "
We are given two points:
(1#200)
and
(4#395)
These mean:
After 1hour, the vehicle is 200miles away.
After 4hours, the vehicle is 395miles away.
First, find the rate of change:
m=(395-200)/(4-1)
m=195/3
m=65
So the vehicle is moving away from the town at a rate of:
65 " miles per hour "
Now the function has the form:
d(t)=65t+b
Use the point (1#200)to find b:
200=65(1)+b
200=65+b
b=135
Therefore, the function is:
d(t)=65t+135
Check using t=4:
d(4)=65(4)+135
d(4)=260+135
d(4)=395
NEW QUESTION # 74
The number of property sales in a region this year is expected to be 3 times the number of property sales in the region last year. The function H(x) represents the number of property sales this year, where x represents 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 280?
Answer: D
Explanation:
This problem uses function notation to describe a multiplicative relationship. The input x is the number of properties sold last year, and the output H(x) is the expected number sold this year. Since this year's sales are
3 times last year's sales, the function rule is H(x)=3x. The given input is 280 because 280 properties were sold last year. Substituting gives H(280)=3(280)=840. That means 840 property sales are expected this year. The answer choice must show the correct input of 280 and the correct output of 840. The other options either reverse the values or use an incorrect output. Therefore, the correct answer is C.
NEW QUESTION # 75
The graph shows the estimated wait time, in minutes, based on the number of hours after 7:00 a.m.
What is the average rate of change of the wait time from point Ato point B?
Answer: C
Explanation:
From the graph, the horizontal axis represents:
t= " hours after 7:00 a.m. "
The vertical axis represents:
" estimated wait time in minutes "
Point Ais approximately at:
A=(5,88.3)
Point Bis approximately at:
B=(9,65)
The average rate of change from point Ato point Bis calculated using:
(y_2-y_1)/(x_2-x_1 )
Substitute the values:
(65-88.3)/(9-5)
=(-23.3)/4
=-5.825
Rounded to two decimal places:
-5.83
So, the wait time decreases by about:
5.83 " minutes per hour "
NEW QUESTION # 76
......
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