MAC1105
Lecture Worksheet 3
Sections 3.13.3
Fall, 2011
1.
The manager of a 200unit apartment complex knows from experience that she can rent every
unit if the rent is $700 per month, but on average, one unit will remain unrented for each $10
increase in the rent. Examine the table before proceeding.
# of $10
increases
x
Monthly Rent ($)
# of units rented
Total Monthly Revenue ($)
R(x)
0
700 + 10(0) = $700
200

0 = 200
(700)(200) = $140,000
1
700 + 10(1) = $710
200

1 = 199
(710)(199) = $141,290
2
700 + 10(2) = $720
200

2 = 198
(720)(198) = $142,560
vertellipsis
vertellipsis
vertellipsis
vertellipsis
50
700 + 10(50) = $1200
200

50 = 150
(1200)(150) = $180,000
vertellipsis
vertellipsis
vertellipsis
vertellipsis
100
700 + 10(100) = $1700
200

100 = 100
(1700)(100) = $170,000
vertellipsis
vertellipsis
vertellipsis
vertellipsis
199
700 + 10(199) = $2690
200

199 = 1
(2690)(1) = $2690
200
700 + 10(200) = $2700
200

200 = 0
(2700)( 0) = $0
a)
Complete the table below by writing expressions that represent the monthly rent, the
number of units rented, and the revenue when the rent is raised by 10 dollars
x
times.
x
R(x)
=
b)
Sketch the graph of the quadratic revenue function R(x). Find both coordinates of the
maximum point, and interpret this point in context.
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 Fall '08
 Algebra, Quadratic equation, $0, $700, $141,290

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