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| Section | Objectives |
|---|---|
| Polynomial and Rational Expressions | - Polynomials
|
| Linear Functions and Systems | - Systems of Equations
|
| Foundations of Algebra | - Equations and Inequalities
|
| Functions and Graphs | - Graphing Functions
|
| Exponential and Logarithmic Concepts | - Logarithmic Basics
|
>> Applied-Algebra Exam Guide <<
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NEW QUESTION # 106
Consider the graph of p(t)shown. The function represents the number of active players, p, in a game thours after 11:00 a.m.
Which interpretation of the concavity between t=0.4and t=3.6is correct?
Answer: C
Explanation:
The graph represents:
p(t)= " number of active players "
where:
t= " hours after 11:00 a.m. "
We need to interpret the concavity between:
t=0.4
and
t=3.6
On this interval, the graph is rising, so the number of players is increasing.
But as the graph rises, it begins to level off near the top. This means the rate of increase is getting smaller.
So the number of players is not increasing faster and faster. Instead, it is increasing, but more slowly as time passes.
That means the graph is concave down on this interval.
The correct interpretation is:
" The number of players is increasing slower and slower. "
NEW QUESTION # 107
A vehicle is travelling away from a rest stop. The function
D(t)=48t+23
represents the distance from the vehicle to the rest stop at time t, where t is measured in hours and D is measured in miles.
What is the value of D(1.7)?
Answer: C
Explanation:
The function is:
D(t)=48t+23
This is a linear function because it has the form:
D(t)=mt+b
where:
48
is the rate of change, and:
23
is the starting distance from the rest stop.
We need to find:
D(1.7)
That means substitute:
t=1.7
into the function.
D(1.7)=48(1.7)+23
First multiply:
48(1.7)=81.6
Now add 23:
D(1.7)=81.6+23
D(1.7)=104.6
So the vehicle is:
104.6 miles
from the rest stop after 1.7 hours.
NEW QUESTION # 108
The number of employees under supervisor B is 13 more than the number of employees under supervisor A.
Let F(n)represent the number of employees under the two supervisors, where nis the number of employees under supervisor A and Fis the number of employees under supervisor B.
Which is the correct function to represent this relationship?
Answer: A
Explanation:
We are told that supervisor B has 13 more employees than supervisor A.
Let:
n= " number of employees under supervisor A "
and
F(n)= " number of employees under supervisor B "
The phrase "13 more than" means we add 13:
F(n)=n+13
So, if supervisor A has nemployees, supervisor B has 13 additional employees.
For example, if supervisor A had 20 employees, then supervisor B would have:
F(20)=20+13=33
Therefore, the correct answer is:
# ( " C " )
NEW QUESTION # 109
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: A
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 # 110
A researcher collected data on the traffic frequency on a section of road. The results are shown in the scatterplot. A regression function is graphed with r
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