Question 1137125: A baseball team plays in a stadium that holds 50000 spectators. When the ticket price is $10, the average attendance is 27000. When the price is lowered to $6, the average attendance rose to 39000.
Find a demand function, D(q), where q is the quantity or number of spectators and D(q) is linear.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! looks like the demand is based on the price.
you have two points to consider.
let x equal the price and y equal the average attendance.
the two points are (x1,y1) = (10,27000)and (x2,y2) = (6,39000)
the slope of a straight line is equal to (y2-y1) / (x2-x1) = (39000 - 27000) / (6 - 10) which is equal to 12000 / -4 which is equal to -3000.
the slope intercept form of the equation of a straight line is y = mx + b.
m is the slope and b is the y-intercept.
replace m with -3000 and the equation becomes y = -3000 * x + b.
to solve for b, replace x and y with the value of one the points on the line.
i chose (6,39000).
y = -3000 * x + b becomes 39000 = -3000 * 6 + b
simplify to get 39000 = -18000 + b.
add 18000 to both sides of this equation to get 39000 + 18000 = b.
solve for b to get b = 57000.
the equation becomes y = -3000 * x + 57000.
y is the demand and x is the price.
let t = d(x) and the equation becomes d(x) = -3000 * x + 57000.
this can also be shown as d(x) = 57000 - 3000 * x.
based on this equation , .....
when x = 0, the price is 0 and the demand will be 57000 which will be more than the stadium can hold because the stadium can only hold 50,000.
when x = 6, the price is 6 and the demand is 57000 - 18000 = 39000.
when x = 10, the price is 10 and the demand is 57000 - 30000 = 27000.
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