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| Section | Objectives |
|---|---|
| Topic 1: Functions and Algebra of Functions | - Derive conclusions based on data - Derive conclusions based on graphs - Derive conclusions based on notation |
| Topic 2: Validity of Models | - Determine fit - Examine utility - Determine validity |
| Topic 3: Graphical Depictions | - Interpret asymptotes for situations - Interpret inputs and outputs for situations - Interpret maximum and minimum for situations - Interpret rates of change for situations - Interpret concavity for situations |
| Topic 4: Logistic Functions | - Interpret inputs and outputs for logistic functions - Interpret asymptotes for logistic functions - Interpret rates of change for logistic functions |
| Topic 5: Linear Functions | - Interpret rates of change for linear functions - Interpret inputs and outputs of linear functions |
| Topic 6: Polynomial Functions | - Interpret inputs and outputs for polynomial functions - Interpret rates of change for polynomial functions - Interpret concavity for polynomial functions |
| Topic 7: Exponential Functions | - Interpret concavity for exponential functions - Interpret inputs and outputs for exponential functions - Interpret rates of change for exponential functions |
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NEW QUESTION # 86
The number of comments on a social media post is represented by the logistic function f(x), whose graph is shown, where xrepresents the number of days since the post was created and f(x)represents the number of comments on day x.
How does the number of comments change as time progresses from day 1 to day 17?
Answer: C
Explanation:
This graph represents a logistic growth function, which has an S-shaped curve.
Key behavior of logistic functions:
Initial phase (early time) # growth is slow
Middle phase # growth speeds up (increasing rate)
Later phase # growth slows down as it approaches a maximum
Analyze the interval from day 1 to day 17:
This interval is in the early part of the graph.
The curve is increasing and getting steeper over this range.
That means the rate of increase is growing over time.
So, the number of comments is:
" increasing faster and faster "
NEW QUESTION # 87
A new company just launched and is using the function M(t)to predict its market share after tyears. The graph of M(t)is shown.
When should the company expect to have a market share of 60%?
Answer: A
Explanation:
The function M(t)represents the company's predicted market share after tyears.
The horizontal axis represents:
t= " time in years "
The vertical axis represents:
M(t)= " market share percentage "
We need to find when the company's market share reaches:
60%
To answer this from the graph:
Locate 60on the vertical axis.
Move horizontally until reaching the blue curve.
Move downward to the horizontal axis to read the corresponding time.
From the graph, the blue curve reaches 60%a little after 6years, approximately at:
t=6.6
So the company should expect to have a market share of 60%after about:
6.6 " years "
NEW QUESTION # 88
The weight of a radioactive sample is given by the function
W(x)=740× # 0.87 #
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