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1105_LW3_3.1-3.3_F11 - MAC1105 Lecture Worksheet 3 Sections...

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MAC1105 Lecture Worksheet 3 Sections 3.1-3.3 Fall, 2011 1. The manager of a 200-unit 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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