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| Section | Objectives |
|---|---|
| Topic 1: Functions and Graphs | - Function Concepts
|
| Topic 2: Exponential and Logarithmic Concepts | - Logarithmic Basics
|
| Topic 3: Polynomial and Rational Expressions | - Rational Expressions
|
| Topic 4: Linear Functions and Systems | - Systems of Equations
|
| Topic 5: Foundations of Algebra | - Algebraic Expressions
|
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NEW QUESTION # 88
After a water tank starts leaking, the amount of water in the tank is modeled by the exponential function that is graphed.
Which statement is justified considering the location of the horizontal asymptote?
Answer: B
Explanation:
The graph shows the water volume decreasing over time.
The vertical axis represents:
" Water volume in gallons "
The horizontal axis represents:
" Time in minutes "
The graph is an exponential decay curve. It decreases quickly at first, then levels off.
From the graph, the curve approaches a horizontal value near:
y=1,000
This means the horizontal asymptote is approximately:
y=1,000
Since the graph approaches 1,000 gallons, it will not decrease to 500 gallons according to this model.
The water volume does not change by a constant rate because exponential functions do not have constant additive change. Also, the graph decreases fastest at the beginning, not later.
NEW QUESTION # 89
The graph shows the number of customers, C(t), showing up to a store, where the number of hours since opening is along the horizontal axis and the number of customers showing up to the store each hour is along the vertical axis.
How can the concavity be described from t=6.2to t=10.1?
Answer: C
Explanation:
From t=6.2to about t=8.5, the graph is increasing, but it is becoming less steep as it approaches a local maximum.
That means the number of customers is:
" increasing slower and slower "
After the local maximum, from about t=8.5to t=10.1, the graph begins to decrease and becomes steeper downward.
That means the number of customers is:
" decreasing faster and faster "
So the full description is:
" The number of customers increases slower and slower and then decreases faster and faster. " Therefore, the correct answer is:
# ( " D " )
NEW QUESTION # 90
The function f(z) represents the relationship between the number of units in two inventories, where z is the number of units in inventory A and f(z) is the number of units in inventory B. The number of units in inventory B is 2 more than the number of units in inventory A. Which function represents this situation?
Answer: B
Explanation:
This problem translates a verbal statement into function notation. The variable z represents the number of units in inventory A, and f(z) represents the number of units in inventory B. The phrase "2 more than" tells us to add 2 to the number of units in inventory A. That gives the rule f(z)=z+2. For example, if inventory A has
10 units, then inventory B has f(10)=12 units. Option A subtracts 2, option C multiplies by 2, and option D divides by 2, so those do not match the stated relationship. Because inventory B is always exactly 2 more than inventory A, the correct function is f(z)=z+2. Therefore, the answer is B.
NEW QUESTION # 91
As regulations change, the number of licensed sellers of a product decreases. The graph models the change in the number of licensed sellers over time.
What does the horizontal asymptote mean?
Answer: A
Explanation:
The horizontal asymptote describes the long-term behavior of the function. In this problem, the graph shows a decreasing exponential model for the number of licensed sellers. The graph begins near a higher value and then decreases, eventually leveling off near 300. This means the number of licensed sellers approaches 300 over time. It does not mean the number necessarily becomes exactly 300 at 21 months, and it does not mean the sellers increase back to the initial value. The initial value is separate from the horizontal asymptote. Since the graph levels off around 300, the correct interpretation is that in the long run, the number of licensed sellers nears 300. Therefore, the answer is C.
NEW QUESTION # 92
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: A
Explanation:
To determine which town's population is growing faster, compare the slopes of the two lines. In a linear population model, the slope represents the growth rate, while the starting value represents the initial population. The graph shows that Town A and Town B both increase over time, but Town B has the larger slope. Town B grows at about 1.3 thousand people per year, while Town A grows at about 1.1 thousand people per year. Since 1.3 > 1.1, Town B's population is increasing at a faster rate. The values 6.5 and 5.5 describe starting population amounts, not growth rates. Therefore, the correct answer is A.
NEW QUESTION # 93
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