7.An amusement park charges $8 admission and average of 2000 visitors per day. A survey shows that , for each $1 increase in the admission cost, 100 fewer people would visit the park.
b.Find the coordinates of the maximum point of this function

Question

7.An amusement park charges $8 admission and average of 2000 visitors per day. A survey shows that , for each $1 increase in the admission cost, 100 fewer people would visit the park.
b.Find the coordinates of the maximum point of this function

anonymous · Answer

we need a quadratic function to start

anonymous · Answer

at present they make $8\times 2000=\$16000$
what happens if they charge $9 ?
they will make $1 more per person, but have 100 fewer people, so they will make 
$$9\times 1990=\$17910$$

anonymous · Answer

suppose they charge $10?  then they make $2 more per person, but have 200 fewer people, make 
$$10\times 1980=\$19800$$

now lets cut to the chase

anonymous · Answer

if they charge say $x$ more dollars they make $x+8$ per person, but have $2000-10x$ customers for a total amount of money as 
$$(x+8)(2000-10x)$$
that is your quadratic function
maximum is at the vertex

anonymous · Answer

you good from there?