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Example 3
Graph both functions up to the year 2008 and describe their trends The total revenue can be modelled by the composite function R(t)=[3C(t)+2T(t)](1.04ⁿ). Find the revenue, create and graphical model and interpret the trend. The number on CD’s sold from 1990 to 1999 started at 3000 and ended at 5000. Once the sales hit 5083 (the maximum of the curve), in 1999 they started to decrease. a) y=-0.03t²+0.5t+3 They stopped selling completely in 2005, when the graph reaches 0. y=1.5-0.1t 1999
Graph both functions up to the year 2008 and describe their trends The total revenue can be modelled by the composite function R(t)=[3C(t)+2T(t)](1.04ⁿ). Find the revenue, create and graphical model and interpret the trend. C(t)=(-0.03t²+0.5t+3)	T(t)=(1.5-0.1t) b)  R(t)   =[3C(t)+2T(t)](1.04ⁿ) =[3(-0.03t²+0.5t+3)+2(1.5-0.1t)](1.04t) =(-0.09t²+1.5t+9+3-0.2t)(1.04t) =(-0.09t²+1.3t+12)(1.04t) 24,000 ­ The maximum revenue from 2000 to 2001 was about $24,000 y=(-0.09t²+1.3t+12)(1.04t)

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Example 2

  • 2. Graph both functions up to the year 2008 and describe their trends The total revenue can be modelled by the composite function R(t)=[3C(t)+2T(t)](1.04ⁿ). Find the revenue, create and graphical model and interpret the trend. The number on CD’s sold from 1990 to 1999 started at 3000 and ended at 5000. Once the sales hit 5083 (the maximum of the curve), in 1999 they started to decrease. a) y=-0.03t²+0.5t+3 They stopped selling completely in 2005, when the graph reaches 0. y=1.5-0.1t 1999
  • 3. Graph both functions up to the year 2008 and describe their trends The total revenue can be modelled by the composite function R(t)=[3C(t)+2T(t)](1.04ⁿ). Find the revenue, create and graphical model and interpret the trend. C(t)=(-0.03t²+0.5t+3) T(t)=(1.5-0.1t) b) R(t) =[3C(t)+2T(t)](1.04ⁿ) =[3(-0.03t²+0.5t+3)+2(1.5-0.1t)](1.04t) =(-0.09t²+1.5t+9+3-0.2t)(1.04t) =(-0.09t²+1.3t+12)(1.04t) 24,000 ­ The maximum revenue from 2000 to 2001 was about $24,000 y=(-0.09t²+1.3t+12)(1.04t)