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| Section | Objectives |
|---|---|
| Topic 1: Polynomial and Rational Expressions | - Polynomials
|
| Topic 2: Functions and Graphs | - Function Concepts
|
| Topic 3: Linear Functions and Systems | - Linear Equations
|
| Topic 4: Exponential and Logarithmic Concepts | - Exponential Functions
|
| Topic 5: Foundations of Algebra | - Equations and Inequalities
|
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NEW QUESTION # 24
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: B
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 # 25
The weight of a radioactive sample is given by the function
W(x)=740× # 0.87 #
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