...... The rise of digital music and the improvement of the DVD format are some
ID: 2962088 • Letter: #
Question
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The rise of digital music and the improvement of the DVD format are some of the reasons why the average selling price of stand-alone DVD recorders will drop in the coming years. The function A(t) = 699/(t + 1)0.94(0 t 5) gives the projected average selling price (in dollars) of stand-alone DVD recorders in year t, where t = 0 corresponds to the beginning of 2002. How fast was the average selling price of stand-alone DVD recorders changing at the beginning of 2002? What was the average selling price of stand-alone DVD recorders in 2002? How fast was the average selling price of stand-alone DVD recorders changing at the beginning of 2006? What was the average selling price of stand-alone DVD recorders in 2006?Explanation / Answer
1) A'(t) = -0.94*699*{ (t+1)^-1.94 } = -657.06*{ (t+1)^-1.94 }
at beginning of 2002, t= 0,
A'(0) = -657.06*{ (0+1)^-1.94 } = -657.06*1 = -657.06
2) average selling price in 2002, A(t=0) = 699/{ (0+1)^0.94 } = $699
3) at beginning of 2006, t= 4,
A'(4) = -657.06*{ (4+1)^-1.94 } = -657.06* 0.044055 = -28.94
d) average selling price in 2006, A(t=4) = 699/{ (4+1)^0.94 } = $153.97
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