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| Section | Objectives |
|---|---|
| Topic 1: Polynomial and Rational Expressions | - Polynomials
|
| Topic 2: Exponential and Logarithmic Concepts | - Logarithmic Basics
|
| Topic 3: Linear Functions and Systems | - Systems of Equations
|
| Topic 4: Functions and Graphs | - Function Concepts
|
| Topic 5: Foundations of Algebra | - Equations and Inequalities
|
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NEW QUESTION # 97
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: B
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 # 98
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?
Answer: D
Explanation:
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 " )
NEW QUESTION # 99
The spread of two viruses within a single population is modeled using the functions in the graph.
What is a correct conclusion based on the graph?
Answer: D
Explanation:
The graph compares the spread of two viruses over time.
The horizontal axis represents:
" time in months "
The vertical axis represents:
" percent of the population affected "
The graph shows:
Virus A as the solid blue curve.
Virus B as the dashed blue curve.
To determine which statement is correct, compare when each virus reaches the same population percentage.
At 20%, Virus A reaches that level earlier than Virus B. The solid curve is already at 20%before the dashed curve reaches 20%.
However, for higher percentages like 70%and 80%, Virus B reaches those levels before Virus A because the dashed curve becomes steeper and rises above the solid curve after about 50%.
So the correct conclusion is:
" Virus A affects " 20% " of the population before virus B does. "
Therefore, the correct answer is:
# ( " A " )
NEW QUESTION # 100
Through a local marketplace, a person makes livestock feeders to sell. The graph shows the functions modeling the cost and revenue.
What is the minimum number of livestock feeders that must be sold in order for the revenue to cover the costs?
Answer: B
Explanation:
This question asks for the break-even point, which is the point where:
Revenue=Cost
On the graph:
The solid blue line represents revenue.
The dashed blue line represents cost.
The revenue line starts below the cost line, meaning the person is not yet covering costs. The revenue line eventually crosses the cost line at a little more than 4 units.
Since the question asks for the minimum number of livestock feeders that must be sold, we need a whole number of feeders.
The graph shows the intersection occurs between:
4 and 5
So selling 4 feeders is not enough, but selling 5 feeders is enough for revenue to cover the costs.
Therefore, the correct answer is:
C
NEW QUESTION # 101
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 #