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| Section | Objectives |
|---|---|
| Foundations of Algebra | - Equations and Inequalities
|
| Linear Functions and Systems | - Systems of Equations
|
| Exponential and Logarithmic Concepts | - Exponential Functions
|
| Polynomial and Rational Expressions | - Rational Expressions
|
| Functions and Graphs | - Function Concepts
|
>> Exam Sample Applied-Algebra Questions <<
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NEW QUESTION # 36
The population of fish in a lake is changing according to the function
P(t)=462-35t
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: C
Explanation:
The function is:
P(t)=462-35t
This is a linear function in the form:
P(t)=mt+b
where:
m= " rate of change "
and
b= " initial value "
In this function:
m=-35
The negative sign means the fish population is decreasing.
The number 35tells us the amount of decrease per month.
So the fish population is decreasing by:
35 " fish per month "
The value 462is not the rate of change. It represents the starting fish population at the beginning of the year, when t=0:
P(0)=462
Therefore, the correct interpretation is:
" The number of fish in the lake is decreasing at a constant rate of 35 fish per month. " So the correct answer is:
# ( " D " )
NEW QUESTION # 37
A contractor charges a flat rate plus a fixed rate per hour to come and make repairs. For a job that takes 3 hours, the contractor charges $220. For a job that takes 5 hours, the contractor charges $340.
Which function correctly represents the total charge Cfor a job that takes thours?
Answer: C
Explanation:
The contractor charges a flat rate plus a fixed rate per hour, so this situation is modeled by a linear function:
C(t)=mt+b
where:
m= " hourly rate "
and
b= " flat rate "
We are given two points:
(3#220)
and
(5#340)
These mean:
A 3-hour job costs $220.
A 5-hour job costs $340.
First, find the hourly rate using slope:
m=(340-220)/(5-3)
m=120/2
m=60
So the contractor charges:
$60 " per hour "
Now the function has the form:
C(t)=60t+b
Use the point (3#220)to find the flat rate:
220=60(3)+b
220=180+b
b=40
So the function is:
C(t)=60t+40
Check with t=5:
C(5)=60(5)+40
C(5)=300+40
C(5)=340
This matches the given information.
NEW QUESTION # 38
The function P(t)represents the yearly profit, in millions of dollars, for a streaming service since opening. The graph of P(t)is shown.
What is the correct interpretation of the maximum value?
Answer: B
Explanation:
The graph represents yearly profit as a function of time:
P(t)= " yearly profit "
where:
t= " years since opening "
The graph is a downward-opening curve, so its maximum value occurs at the highest point, also called the vertex.
From the graph, the highest point occurs at approximately:
t=10.5
So the maximum yearly profit happened approximately:
10.5 " years after opening "
The vertical axis measures yearly profit in millions of dollars. From the graph, the maximum value is approximately:
1.41
Since the units are millions of dollars:
1.41×1,000,000=1,410,000
So the maximum yearly profit was approximately:
$1,410,000
Therefore, the correct answer is:
# ( " C " )
NEW QUESTION # 39
The number of tasks completed by computer B is 12 more than the number of tasks completed by computer A. Let F(x)represent the relationship between the number of tasks completed by the two computers, where xis the number of tasks completed by computer A and Fis the number of tasks completed by computer B.
Which function represents this situation?
Answer: A
Explanation:
We are told that computer B completes 12 more tasks than computer A.
Let:
x= " number of tasks completed by computer A "
and
F(x)= " number of tasks completed by computer B "
The phrase "12 more than" means add 12 to the original amount:
F(x)=x+12
So, if computer A completes xtasks, computer B completes:
x+12
tasks.
For example, if computer A completed 50 tasks, then computer B completed:
F(50)=50+12=62
Therefore, the correct answer is:
# ( " B " )
NEW QUESTION # 40
A researcher collected data on the number of daily posts on a blog. The results are shown in the scatterplot.
The graphed regression function has an r
2
value of 0.89.
Is it appropriate to make a prediction for the number of daily posts after 18.6 months?
Answer: B
Explanation:
The value r2=0.89 indicates a strong fit because it is close to 1. A strong fit means the regression function follows the scatterplot data closely enough to support reasonable prediction. The question asks whether a prediction at x=18.6 months is appropriate. This value is outside the observed data range, so the prediction involves extrapolation. For a strong regression model, extrapolation can be acceptable if the new x-value is not too far beyond the maximum observed value. Here, x=18.6 is within 50% of the range beyond the maximum value, so the prediction is considered appropriate. Therefore, the correct answer is C.
NEW QUESTION # 41
......
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