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| Section | Objectives |
|---|---|
| Topic 1: Exponential Functions | - Interpret concavity for exponential functions - Interpret rates of change for exponential functions - Interpret inputs and outputs for exponential functions |
| Topic 2: Validity of Models | - Determine fit - Determine validity - Examine utility |
| Topic 3: Graphical Depictions | - Interpret maximum and minimum for situations - Interpret rates of change for situations - Interpret inputs and outputs for situations - Interpret asymptotes for situations - Interpret concavity for situations |
| Topic 4: Polynomial Functions | - Interpret rates of change for polynomial functions - Interpret concavity for polynomial functions - Interpret inputs and outputs for polynomial functions |
| Topic 5: Logistic Functions | - Interpret rates of change for logistic functions - Interpret asymptotes for logistic functions - Interpret inputs and outputs for logistic functions |
| Topic 6: Linear Functions | - Interpret rates of change for linear functions - Interpret inputs and outputs of linear functions |
| Topic 7: 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 # 100
The scatterplot shows data on the number of shirts sold at a gift shop per week over time. The graphed regression function has an r
2
value of 0.09.
Which range of x-values is appropriate for extrapolation?
Answer: B
Explanation:
The r
2
value tells how closely the regression model fits the scatterplot data. In this problem, r
2
=0.09, which is extremely low. This means the regression model explains only a very small portion of the variation in the shirt-sales data. When r
2
is this weak, the model is not reliable for predictions outside the data range. Extrapolation is already less certain than interpolation because it predicts beyond the observed data. With such a poor fit, extending the model beyond the data would not be appropriate. Since 0.09 < 0.3, the best justification is that extrapolation is not appropriate because r
2
< 0.3. Therefore, the correct answer is C.
NEW QUESTION # 101
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: B
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 # 102
The graph shows the total cost of a lumber delivery based on the number of identical boards ordered.
What is the cost of each additional board?
Answer: A
Explanation:
The graph shows a linear relationship between:
" Number of boards "
and
" Total cost "
The cost of each additional board is the rate of change, or slope, of the line.
From the graph, two labeled points are:
(0#27)
and
(10#177)
This means:
When 0 boards are ordered, the total cost is $27.
When 10 boards are ordered, the total cost is $177.
Now calculate the slope:
m=(177-27)/(10-0)
m=150/10
m=15
So each additional board costs:
$15
Therefore, the correct answer is:
# ( " B " )
NEW QUESTION # 103
An exponential growth function can be used to model the number of bacteria in a population. The function G(t)=1,600× # 1.31 #
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