. Henri Roulant (of “Roulant's Band") recently broke into acting. Henri realizes that the number of tickets that will be bought for opening night of the his movie premiere is a function of the amount money spent on advertising the week leading up to the movie. Let T(d) be the number of tickets that will be bought for opening night if d dollars are spent on advertising that week. Henri models T(d) using the formula T(d) = 20 log(d+ 20) + 400. For any equations that need to be solved in this problem, make sure that you solve them algebraically by hand, showing each step in the process. Give you answers both in exact form and rounded in a way that makes sense in the context of the problem. a) How many tickets does Henri expect will be bought if no money is spent on advertising during that week? b) How many tickets does Henri expect will be bought if $18, 880 are spent on advertising during that week? c) The movie is a success if 600 tickets are sold. How much money does Henri's model indicate should be spent on advertising that week for the movie to be considered successful?
. Henri Roulant (of “Roulant's Band") recently broke into acting. Henri realizes that the number of tickets that will be bought for opening night of the his movie premiere is a function of the amount money spent on advertising the week leading up to the movie. Let T(d) be the number of tickets that will be bought for opening night if d dollars are spent on advertising that week. Henri models T(d) using the formula T(d) = 20 log(d+ 20) + 400. For any equations that need to be solved in this problem, make sure that you solve them algebraically by hand, showing each step in the process. Give you answers both in exact form and rounded in a way that makes sense in the context of the problem. a) How many tickets does Henri expect will be bought if no money is spent on advertising during that week? b) How many tickets does Henri expect will be bought if $18, 880 are spent on advertising during that week? c) The movie is a success if 600 tickets are sold. How much money does Henri's model indicate should be spent on advertising that week for the movie to be considered successful?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:1. Henri Roulant (of "Roulant's Band") recently broke into acting. Henri realizes that the number
of tickets that will be bought for opening night of the his movie premiere is a function of the
amount money spent on advertising the week leading up to the movie. Let T(d) be the number
of tickets that will be bought for opening night if d dollars are spent on advertising that week.
Henri models T(d) using the formula
T(d) = 20 log(d+ 20) + 400.
For any equations that need to be solved in this problem, make sure that you solve them
algebraically by hand, showing each step in the process. Give you answers both in exact form
and rounded in a way that makes sense in the context of the problem.
a) How many tickets does Henri expect will be bought if no money is spent on advertising
during that week?
b) How many tickets does Henri expect will be bought if $18, 880 are spent on advertising
during that week?
c) The movie is a success if 600 tickets are sold. How much money does Henri's model indicate
should be spent on advertising that week for the movie to be considered successful?
d) Henri realizes that on opening night "Roulant's Band" is also scheduled to perform a
concert. The number of concert tickets sold to see the band is given by the function
C(d) = 40 log((d + 20)²) + 100,
where d is the number of dollars that the band spends on advertising the concert during
the week leading up to the concert. If both the band and the movie company hope to
spend the same amount of advertising money and sell the same number of tickets, how
much should they spend during the week? Will Henri's movie be a success?
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