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| Section | Objectives |
|---|---|
| Linear Functions | - Interpret rates of change for linear functions - Interpret inputs and outputs of linear functions |
| Validity of Models | - Determine fit - Examine utility - Determine validity |
| Logistic Functions | - Interpret rates of change for logistic functions - Interpret inputs and outputs for logistic functions - Interpret asymptotes for logistic functions |
| Graphical Depictions | - Interpret concavity for situations - Interpret maximum and minimum for situations - Interpret rates of change for situations - Interpret asymptotes for situations - Interpret inputs and outputs for situations |
| Polynomial Functions | - Interpret inputs and outputs for polynomial functions - Interpret rates of change for polynomial functions - Interpret concavity for polynomial functions |
| Exponential Functions | - Interpret rates of change for exponential functions - Interpret inputs and outputs for exponential functions - Interpret concavity for exponential functions |
| Functions and Algebra of Functions | - Derive conclusions based on graphs - Derive conclusions based on data - Derive conclusions based on notation |
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NEW QUESTION # 132
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: C
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 # 133
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: C
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 # 134
The exponential function
f(x)=280× # 1.08 #
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