Irrerbthist6n

2022-01-17

At a certain school, the number of student tickets sold for a home football game can be modeled by $S\left(p\right)=59p+8100$, where p is the winning percent of the home team. The number of nonstudent tickets sold for these home games is given by $N\left(p\right)=0.2{p}^{2}+12p+4100$.
a. Write an equation T(p) for the total number of tickets sold for a home football game at this school as a function of the winning percent p.
b. What is the domain for the function in part a. in this context?
c. Assuming that the football stadium is filled to capacity when the team wins 90% of its home games, what is the capacity of the school's stadium?

Jenny Bolton

Total of s(p) and n(p) gives the expression for T(p)
Solution: $S\left(p\right)=59p+8100$
$N\left(p\right)=0.2{p}^{2}+12p+4100$
a) Total number of ticket sold $=s\left(p\right)+n\left(p\right)$
$=59p+8100+0.2{p}^{2}+12p+4100$
$=0.2{p}^{2}+71p+12200$
b) As given for pass percent p
$0\le p\le 100$
c) $p=90\mathrm{%}$
$p=90$ its

ol3i4c5s4hr

Consider that the number of student ticket sold for a game is $S\left(p\right)=59p+8100$ and the number of non student ticket sold is given by $N\left(p\right)=0.2{p}^{2}+12p+4100$, here pdenotes the winning percentage.
a) Equation of total number of tickets sold T(p) for the game.
Since total number of ticket sold would be the sum of the tickets sold to both student
and non students therefore, $T\left(p\right)=S\left(p\right)+N\left(p\right)$
$=59p+8100+0.2{p}^{2}+12p+4100$
$=0.2{p}^{2}+71p+12200$
b) Find the domain of the function $T\left(p\right)=0.2{p}^{2}+71p+12200$.
Since T(p) is a polynomial function and the domain of polynomial function is set of real numbers.
Hence domain of $T\left(p\right)=0.2{p}^{2}+71p+12200$ is set of real numbers denoted by R.
c) Given for $p=90\mathrm{%}$ stadium is full. Find the capacity of stadium.
Substitute and solve.
$T\left(p\right)=0.2{\left(0.9\right)}^{2}+71\left(0.9\right)+12200$
$=0.162+63.9+12200$
$=12,264.062$
$\approx 12,264$
Hence the stadium capacity is 12264

alenahelenash

Total number of tickets sold $=\left(\text{total number of student tickets sold}\right)+\left(\text{total number of non-student tickets}\right)$ $=S\left(p\right)+N\left(p\right)$ $=\left(57p+8900\right)+\left(0.2{p}^{2}+17p+4800\right)$ $=0.2{p}^{2}+74p+13700$