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| Section | Objectives |
|---|---|
| Topic 1: Validity of Models | - Examine utility - Determine fit - Determine validity |
| Topic 2: Graphical Depictions | - Interpret rates of change for situations - Interpret maximum and minimum for situations - Interpret asymptotes for situations - Interpret inputs and outputs for situations - Interpret concavity for situations |
| Topic 3: Logistic Functions | - Interpret asymptotes for logistic functions - Interpret rates of change for logistic functions - Interpret inputs and outputs for logistic functions |
| Topic 4: Exponential Functions | - Interpret concavity for exponential functions - Interpret rates of change for exponential functions - Interpret inputs and outputs for exponential functions |
| Topic 5: Functions and Algebra of Functions | - Derive conclusions based on notation - Derive conclusions based on graphs - Derive conclusions based on data |
| Topic 6: Polynomial Functions | - Interpret concavity for polynomial functions - Interpret rates of change for polynomial functions - Interpret inputs and outputs for polynomial functions |
| Topic 7: Linear Functions | - Interpret inputs and outputs of linear functions - Interpret rates of change for linear functions |
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問題 #42
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?
答案：D
解題說明：
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.
問題 #43
After a water tank starts leaking, the amount of water in the tank is modeled by the exponential function that is graphed.
Which statement is justified considering the location of the horizontal asymptote?
答案：D
解題說明：
The graph shows the water volume decreasing over time.
The vertical axis represents:
" Water volume in gallons "
The horizontal axis represents:
" Time in minutes "
The graph is an exponential decay curve. It decreases quickly at first, then levels off.
From the graph, the curve approaches a horizontal value near:
y=1,000
This means the horizontal asymptote is approximately:
y=1,000
Since the graph approaches 1,000 gallons, it will not decrease to 500 gallons according to this model.
The water volume does not change by a constant rate because exponential functions do not have constant additive change. Also, the graph decreases fastest at the beginning, not later.
問題 #44
The exponential function
f(x)=280× # 1.08 #