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| Section | Objectives |
|---|---|
| Logistic Functions | - Interpret asymptotes for logistic functions - Interpret rates of change for logistic functions - Interpret inputs and outputs for logistic functions |
| Validity of Models | - Examine utility - Determine fit - Determine validity |
| Functions and Algebra of Functions | - Derive conclusions based on notation - Derive conclusions based on data - Derive conclusions based on graphs |
| Linear Functions | - Interpret rates of change for linear functions - Interpret inputs and outputs of linear functions |
| Polynomial Functions | - Interpret concavity for polynomial functions - Interpret inputs and outputs for polynomial functions - Interpret rates of change for polynomial functions |
| Graphical Depictions | - Interpret maximum and minimum for situations - Interpret asymptotes for situations - Interpret concavity for situations - Interpret inputs and outputs for situations - Interpret rates of change for situations |
| Exponential Functions | - Interpret concavity for exponential functions - Interpret rates of change for exponential functions - Interpret inputs and outputs for exponential functions |
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NEW QUESTION # 40
Consider the function I(m)=41m²#490m+30, which represents the daily income, I, in dollars, of a store based on the number of months, m, since the beginning of the year. What is the difference between I(7) and I(9)?
Answer: C
Explanation:
This is a polynomial function evaluation problem. Since I(m) represents daily income in dollars, the difference between I(7) and I(9) must also be in dollars. First evaluate I(7)=41(49)#490(7)
+30=2009#3430+30=#1391. Then evaluate I(9)=41(81)#490(9)+30=3321#4410+30=#1059. The difference is
|#1059#(#1391)|=332. Because the question asks for the difference between the two outputs, the correct unit is dollars, not months. So the difference between I(7) and I(9) is approximately $332. Therefore, the correct answer is C.
NEW QUESTION # 41
The population of fish in a lake is changing according to the function
P(t)=462-35t
where tis the number of months since the beginning of the year and P(t)is the fish population at time t.
Which interpretation of the rate of change is correct?
Answer: B
Explanation:
The function is:
P(t)=462-35t
This is a linear function in the form:
P(t)=mt+b
where:
m= " rate of change "
and
b= " initial value "
In this function:
m=-35
The negative sign means the fish population is decreasing.
The number 35tells us the amount of decrease per month.
So the fish population is decreasing by:
35 " fish per month "
The value 462is not the rate of change. It represents the starting fish population at the beginning of the year, when t=0:
P(0)=462
Therefore, the correct interpretation is:
" The number of fish in the lake is decreasing at a constant rate of 35 fish per month. " So the correct answer is:
# ( " D " )
NEW QUESTION # 42
The function d(x)=14+65xrepresents the distance, in meters, from a tower to an object at time x, in seconds.
What is the value of d(1.5)?
Answer: B
Explanation:
We are given the function:
d(x)=14+65x
This is a linear function because it has the form:
d(x)=mx+b
where 65is the rate of change and 14is the starting value.
We need to find:
d(1.5)
That means substitute x=1.5into the function:
d(1.5)=14+65(1.5)
Now multiply:
65(1.5)=97.5
Then add:
d(1.5)=14+97.5
d(1.5)=111.5
So the distance from the tower to the object at 1.5seconds is:
111.5 " meters "
NEW QUESTION # 43
The data in the scatterplot represents the number of monthly train crossings at a particular intersection over time.
Which type of function should be used to model the data?
Answer: A
Explanation:
The scatterplot shows the number of monthly train crossings decreasing over time. The decrease is not constant from one year to the next, so a linear model is not the best choice. Instead, the data decreases quickly at first and then begins to level off, which is characteristic of exponential decay. Exponential models are appropriate when a quantity changes by a repeated factor or percentage over equal time intervals. A logistic model would usually show an S-shaped pattern with a carrying capacity, and a polynomial model would be more appropriate for turning points or more complex curvature. Since the points show a smooth decreasing curve that flattens over time, an exponential function best models the data. Therefore, the correct answer is B.
NEW QUESTION # 44
The populations, in thousands, of two towns are shown in the graph, where the horizontal axis measures the time in years.
Which town's population is growing at a faster rate?
Answer: D
Explanation:
To decide which town is growing faster, compare the slopes of the two lines. In a linear population graph, the slope represents the growth rate, while the starting value represents the initial population. The graph shows that Town A has a slope of about 1.0 thousand people per year, while Town B has a slope of about 0.7 thousand people per year. Since 1.0 > 0.7, Town A is growing at a faster rate. The values 6.5 and 5.5 refer to population amounts, not growth rates, so they do not answer the question. The correct comparison must use the slopes. Therefore, the correct answer is D.
NEW QUESTION # 45
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