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| Section | Objectives |
|---|---|
| Logistic Functions | - Interpret asymptotes for logistic functions - Interpret inputs and outputs for logistic functions - Interpret rates of change for logistic functions |
| Exponential Functions | - Interpret rates of change for exponential functions - Interpret inputs and outputs for exponential functions - Interpret concavity for exponential functions |
| Linear Functions | - Interpret inputs and outputs of linear functions - Interpret rates of change for linear functions |
| Functions and Algebra of Functions | - Derive conclusions based on graphs - Derive conclusions based on data - Derive conclusions based on notation |
| Polynomial Functions | - Interpret concavity for polynomial functions - Interpret rates of change for polynomial functions - Interpret inputs and outputs for polynomial functions |
| Graphical Depictions | - Interpret rates of change for situations - Interpret asymptotes for situations - Interpret maximum and minimum for situations - Interpret concavity for situations - Interpret inputs and outputs for situations |
| Validity of Models | - Examine utility - Determine validity - Determine fit |
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質問 # 80
The value of a collectible coin can be modeled by F(t), where t represents years since the number of years since the coin was found, and the vertical axis represents the value, in thousands of dollars.
How is the value of the coin changing over time based on the graph?
正解：A
解説：
The graph shows the value of the coin increasing over time. Since the curve rises from left to right, the value is not decreasing. The graph also becomes steeper as time increases, which means the rate of increase is getting larger. In Applied Algebra, when a graph is increasing and its slope is increasing, the quantity is described as increasing faster and faster. This is typical of exponential growth, where values grow by a repeated percent or factor rather than by a constant amount. The choices involving decreasing are incorrect because the graph moves upward. The choice "increasing slower and slower" would require the graph to flatten, which it does not. Therefore, the correct answer is B.
質問 # 81
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?
正解：D
解説：
The graph compares the populations of two towns over time.
The horizontal axis represents:
" Time in years "
The vertical axis represents:
" Population in thousands "
The graph shows:
Town A as the solid blue line.
Town B as the dashed blue line.
To determine which town's population is growing faster, we compare the slopes of the two lines.
In Applied Algebra, the slope of a line represents the rate of change:
" slope " = " change in population " / " change in time "
From the graph:
" Town A grows at about " 0.9 " thousand people per year "
" Town B grows at about " 1.6 " thousand people per year "
Now compare the growth rates:
1.6 > 0.9
So Town B's population is growing at a faster rate.
The values 8.0and 6.5describe starting populations, not growth rates. Since the question asks about growing at a faster rate, we must compare the slopes.
質問 # 82
The graph shows the daily practice duration for a musician, where the number of days since the beginning of the month is along the horizontal axis and the number of minutes practiced per day is along the vertical axis.
Based on the graph, what was the practice duration for day 8?
正解：D
解説：
This question asks us to interpret a value from a graph.
The horizontal axis represents:
Days
The vertical axis represents:
Practice duration in minutes
We need to find the practice duration on day 8.
To do this:
Locate 8 on the horizontal axis.
Move vertically until you reach the blue graph.
Read the corresponding value on the vertical axis.
From the graph, when:
x=8
the blue graph is at:
y=115
So the musician practiced for:
115 minutes
質問 # 83
A researcher collected data on the average number of product returns per month to a company over time. The results are shown in the scatterplot. The graphed regression function has an r
2
value of 0.45.
Which range of x-values is appropriate for extrapolation?
正解：C
解説：
The coefficient of determination, r
2
, measures how well a regression model fits the data. A value close to 1 indicates a strong fit, while a lower value indicates that the model does not explain the data as reliably. Here, r
2
=0.45, which is below 0.7. That means the model does not have a strong enough fit for reliable extrapolation in this question. Extrapolation means using the model to predict values outside the observed data range, which is riskier than interpolation. Because the model fit is not strong, choosing an extended range of x-values would not be appropriate. The correct reason is that extrapolation is not appropriate because r
2
< 0.7. Therefore, the answer is D.
質問 # 84
The population of fish in a lake is changing according to the function
P(t)=24t+185
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?
正解：C
解説：
The function is:
P(t)=24t+185
This is a linear function in the form:
P(t)=mt+b
where:
m= " rate of change "
and
b= " initial value "
In the function:
P(t)=24t+185
the coefficient of tis:
24
So the rate of change is:
24 " fish per month "
Because 24is positive, the fish population is increasing.
The number 185is not the rate of change. It represents the starting fish population at the beginning of the year, when t=0:
P(0)=24(0)+185=185
Therefore, the correct interpretation is:
" The number of fish in the lake is increasing at a constant rate of 24 fish per month. " So the correct answer is:
# ( " B " )
質問 # 85
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Applied-Algebra試験問題解説集: https://www.japancert.com/Applied-Algebra.html