Consider that the number of student ticket sold for a game is S(p)=59p+8100 and number of non student ticket sold is given by N(p)=0.2p2+12p+4100, here p denotes the winning percentage. a) Equation of total number of tickets sold T(p) for the game. b) Find the domain of the function T(p)=0.2p2+71p+12200 c) Given for p=90% stadium is full. Find the capacity of stadium.

Question

Consider that the number of student ticket sold for a game is S(p)=59p+8100 and number of non student ticket sold is given by N(p)=0.2p2+12p+4100, here p denotes the winning percentage.  a) Equation of total number of tickets sold T(p) for the game.  b) Find the domain of the function T(p)=0.2p2+71p+12200  c) Given for p=90% stadium is full. Find the capacity of stadium.

l1koV · Accepted Answer

Step 1 a) Since total number of ticket sold would be the sum of the tickets sold to both students T(p)=S(p)+N(p) and non students therefore, =59p+8100+0.2p2+12p+4100 Step 2 Since T(p) is a polynomial function and the domain of polynomial function is set of real numbers. Hence domain of T(p)=0.2p2+71p+12200 is set real numbers denoted by R. Step 3 Substitute p=90%=0.9 into T(p)=0.2p2+71p+12200 and solve. T(p)=0.2(0.9)2+71(0.9)+12200 =0.162+63.9+12200 =12.264062  ≈12.264 Hence the stadium capacity is 12264

Consider that the number of student ticket sold for a game is S(p)=59p+8100ZS

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