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| Section | Objectives |
|---|---|
| Topic 1: Validity of Models | - Determine validity - Examine utility - Determine fit |
| Topic 2: Linear Functions | - Interpret rates of change for linear functions - Interpret inputs and outputs of linear functions |
| Topic 3: Polynomial Functions | - Interpret concavity for polynomial functions - Interpret inputs and outputs for polynomial functions - Interpret rates of change for polynomial functions |
| Topic 4: Graphical Depictions | - Interpret rates of change for situations - Interpret concavity for situations - Interpret asymptotes for situations - Interpret maximum and minimum for situations - Interpret inputs and outputs for situations |
| Topic 5: Exponential Functions | - Interpret inputs and outputs for exponential functions - Interpret concavity for exponential functions - Interpret rates of change for exponential functions |
| Topic 6: Functions and Algebra of Functions | - Derive conclusions based on notation - Derive conclusions based on data - Derive conclusions based on graphs |
| Topic 7: Logistic Functions | - Interpret rates of change for logistic functions - Interpret asymptotes for logistic functions - Interpret inputs and outputs for logistic functions |
>> Applied-Algebra Official Study Guide <<
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NEW QUESTION # 46
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: B
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 # 47
The number of acres affected by an invasive species can be modeled using the logistic function f(x), where xrepresents the number of months since the species was introduced and f(x)represents the number of affected acres. The graph of f(x)is shown.
What happens as time progresses from month 2 to month 6?
Answer: A
Explanation:
This is also a logistic growth curve.
Analyze the interval from month 2 to month 6:
The graph is increasing during this time.
The curve is becoming steeper, meaning the slope is increasing.
This indicates the rate of change is getting larger over time.
So, the number of affected acres is:
" increasing faster and faster "
This corresponds to the early-to-middle growth phase of a logistic function.
NEW QUESTION # 48
The values, in dollars, of two accounts over time are modeled by
A_1 (t)=6,500× # 1.05 #
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