a) Find the demand function p(x), where x is the number of the spectators. (Assume that p(x) is linear.)

Question

A baseball team plays in a stadium that holds 50000 spectators. With the ticket price at $9 the average attendance has been 21000. When the price dropped to $8, the average attendance rose to 25000. 

a) Find the demand function p(x), where x is the number of the spectators. (Assume that p(x) is linear.) 

p(x) = _____

Answer 1

(21,9), (25,8) have a line through them with slope = (9-8)/(21-25) = -1/4

P-8 = -(1/4)(x-25) in point slope form

P =-x/4 +25/4 +8

P = -x/4 +6.25+8

P =-x/4 +14.25 is the linear demand curve

with P measured in dollars and x in thousands

and domain 0< x < 50 (thousand)

with zero price x= 14.25(4) = 57>50

for x=50, P=-50/4+14.25 =14.25-12.5= $1.75

range 1.75<P<14.25

at $14.25 no one shows up, zero attendance

although these are averages, so different numbers are possible

or

p(x) =-x/4 +14,250

is the linear demand curve you probably want

it might help to draw a rough sketch of the demand curve

they call it a curve even if it's a straight line