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| Section | Objectives |
|---|---|
| Topic 1: Exponential and Logarithmic Concepts | - Logarithmic Basics
|
| Topic 2: Foundations of Algebra | - Equations and Inequalities
|
| Topic 3: Linear Functions and Systems | - Linear Equations
|
| Topic 4: Polynomial and Rational Expressions | - Polynomials
|
| Topic 5: Functions and Graphs | - Function Concepts
|
>> Test Applied-Algebra Study Guide <<
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NEW QUESTION # 58
An investment account accrues interest every year, and the value of the account is given by G(x). The graph of this function is shown.
What represents the value of the account after 4 years?
Answer: D
Explanation:
The graph represents the value of an investment account over time. The horizontal axis gives time in years, and the vertical axis gives the total account value in dollars. To find the value after 4 years, locate x=4 on the horizontal axis and read the corresponding G(x)-value on the graph. The plotted exponential growth curve is slightly above $1,000 at 4 years, closest to $1,052.87. Because the graph shows an increasing exponential trend, values such as $480.52, $584.62, and $711.28 are too low for the account value at x=4. The correct interpretation is that after 4 years, the investment account is worth approximately $1,052.87. Therefore, the correct answer is D.
NEW QUESTION # 59
A researcher collected data on the number of books donated per month to a thrift store over time. The results are shown in the scatterplot. A regression function is graphed with r
2
=0.99.
Which range of x-values is appropriate for extrapolation?
Answer: A
Explanation:
The value r
2
=0.99 indicates a very strong regression fit because it is close to 1. A strong fit means the model explains most of the variation in the data, so limited extrapolation can be appropriate. However, extrapolation should stay close to the observed data range. From the scatterplot, the data values appear to run from about x=5 to x=15. A reasonable extrapolation range extends slightly beyond those observed values, not too far outside them. The interval x=2.5 to x=17.5 stays close to the original data and is more appropriate than the wider interval x=0 to x=20. Therefore, the correct answer is B.
NEW QUESTION # 60
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: C
Explanation:
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.
NEW QUESTION # 61
The graph shows the number of books, N, checked out from a library each week. The number of weeks since the beginning of the year is on the horizontal axis, and the number of books checked out per week is on the vertical axis. Point A represents 165 books checked out in the first week, or N(0)=165. Which statement represents an accurate conclusion?
Exhibit:
Answer: C
Explanation:
This question asks for the correct interpretation of a labeled point on a graph. In function notation, N(x)=y means when the input is x weeks, the output is y books checked out. The exhibit shows several plotted points.
Point B is located at approximately x=2.8 and y=177, so Point B represents N(2.8)=177. To verify a graph statement, both the horizontal coordinate and vertical coordinate must match the actual point on the graph. If either coordinate is wrong, then the statement is not accurate. Since Point B matches the stated coordinates and output value, it is the valid conclusion. Therefore, the correct answer is A.
NEW QUESTION # 62
A set of data was gathered and used to create a model for the number of subscribers to a blog. The function model is f(x)=190× # 0.99 #