SOLUTION: my question is that: please explain why the function is T(n) = (600-50n)*(10+n) and explain if the function is continuous at a point or not.
in the problem: A school concert usu
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in the problem: A school concert usu
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Question 1132481: my question is that: please explain why the function is T(n) = (600-50n)*(10+n) and explain if the function is continuous at a point or not.
in the problem: A school concert usually attracts 600 people at a cost of $10 per person.
On average for every $1 rise in admission price, 50 less people attend the concert.
If T is the total amount of takings and n is the number of $1 increases write a rule for the function which gives T in terms of n.
my question is related to limits and/or continuity Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! the school concert usually attracts 600 people at a cost of 10 dollars per person.
the function designation of T(n) tells you the total revenue.
revenue is a function of the number of tickets times the price per ticket.
then the number of tickets is 600 and the price per ticket is 10 dollars, then the value of T is equal to 600 * 10 = 6000
the function T(n) tells you what happens when the price of a ticket goes up or down by the value of n.
what happens is that, for every increase in the value of n by 1, the number of tickets sold goes down by 50.
note that, if n is negative, then the equation is telling you that the number of tickets goes up by 50 for every drop in price of 1 dollar.
the following table illustrates what happens when the value of n is changed.
the following graph shows you what the equation looks like on a graph.
the maximum revenue is attained when the value of n is 1.
when that occurs, the number of tickets sold is 550 and the price is 11 dollars a ticket for a total revenue of 6050 dollars.
the table confirms that as well.
the graph is continuous at all points.
there are no discontinuities.
the domain and the range of the graph itself are all real velues of x and y with no constraints.
the practical constraints of the problem give you a domain of x from -10 to 12, with a range of y from 0 to 6050.
that is why the graph is shaded for x <= -10 and x >= 12.
those constraints on x force y to be between 0 and 6050 only.
