# calculus

You are working as assistant to a major movie producer from Hollywood, but mainly you look after pre-release film publicity. You are an old hand at publicity, having worked in several production companies before. Based on previous experience you have developed a model for the most effective expenditure of money in radio and television advertising in the last ten days prior to the release of the film. The advertising campaign starts with massive media blitz ten days before the release of the film. Money spent, (in 100,000 dollars) as a function of the number of days after the initial media blitz, , is given by:

M(n)=(n^3-48n+1100)/200

The producer, your boss, comes in and asks you to prepare a report on the funding needs for Radio and Television advertising in the days between the media blitz and the release, highlighting the rate at which spending goes up or down each day. In particular he seems interested in the rate at which spending will change in the 'th day. To estimate this,using your formula, calculate the average rate of change for each of the following intervals (in 100,000 dollars per day):

Average rate of change on [0,1]:
Average rate of change on [1,2]:
Average rate of change on [2,3]:
Average rate of change on [3,4]:
Average rate of change on [4,5]:
Average rate of change on [5,6]:
Average rate of change on [6,7]:
Average rate of change on [7,8]:
Average rate of change on [8.9]:
Average rate of change on [9,10]:
Why was the manager interested in the 'th day?
a)NO reason
b)Spending starts increasing day after day
c)the day is peak of expenditures
d)Spending starts decreasing day after day

Your best estimate for the instantaneous rate of change at the 4'th day:

please help with this questions...i really don't get how to slve!
mary

1. 👍
2. 👎
3. 👁
1. Well they say estimate so I would not calculate the cubic equation for each day and subtract. I would use the derivative.
Since they want the average rate of change between 0 and 1 for example, I think it appropriate to use the rate of change at the derivative at 0 and the derivative at 1 and average them for 0 - 1
Of course we must get that derivative

M(n)=(n^3-48n+1100)/200
200 M(n) = n^3 - 48 n + 1100
200 dM/dt = 3 n^2 -48
so
rate n = dM/dt = (3 n^2 -48)/200
calculate that at
n = 0
n = 1
n = 2
n = 3 etc
then
rate 0 - 1 = (1/2)( rate 0 + rate 1)

by the way the maximum spending will be when dM/dt = 0
3 n^2 - 48 = 0
n^2 = 16
n = 4
That is why they want you to calculate M there and that is why the boss wants to know these rates.

1. 👍
2. 👎
2. By the way, I would personally program a spreadsheet to do those numbers, but a fancy programable calculator would do it pretty fast.

1. 👍
2. 👎

## Similar Questions

1. ### math

mr. Rodriguez, a college instructor, can grade his class papers in 3 hours while it takes his assistant 4 1/2 hours. If Mr. Rodriguez graded the papers for 1 hour and then left the job for his assistant to complete, how long will

2. ### psy

18. Choose the pair of words/phrases among the choices that exhibits the same logical relationship as the words/phrases in the following pair. conductor : orchestra (Points : 1) skater : rink teacher : principal producer : movie l

3. ### Language Arts

1. Which of these statements reflects subjunctive mood? I wish it were possible to go to the movie tomorrow. If we go to a movie, will I be able to have popcorn?*** She hoped to go to the movie and have popcorn. He couldn't go to

4. ### Finite Math

A producer wants to put on a variety show on television. Assume that the producer has 9 skits and 6 commercials available. In how many ways can the producer create a television show? We assume that a skit is never repeated, but

1. ### math

Alfonso makes \$8.00 per hour working at a movie theater and \$12.00 per hour working at a restaurant. Next week, Alfonso is scheduled to work 6 hours at the movie theater. Which of the following inequalities represents the amount

2. ### Medical Assisting

I need help on this one question! 9. Explain the key training, education, and certification preparation needed for medical assistants? a. The AAMA requires licensure for medical assistants in some states. b. It is optimal for a

3. ### MicroEcon

The market for apple pies in the city is competitive and has the following demand schedule: Price Quantity Demanded \$1 1,200 2 1,100 3 1,000 4 900 5 800 6 700 etc... 13 0 Each producer in the market has fixed costs of \$9 and the

4. ### Math Again helpppp

1. A new movie open the other day. So far 500,000 people have seen. The producers of the movie need to know if the people liked it. A random sample of 8000 people were asked as they were leaving the theater if they like the movie.

1. ### algebra

Members of the student government are planning a movie night on campus. They have asked a random sample of students which of four movies the students would prefer. Here are the results. Movie Preferred Number of Students Movie A

2. ### Language Arts

Which of the following sentences about the selection uses the past perfect tense? A. I have planned to see the movie tomorrow B. I still plan on going to see the movie tomorrow C. I had planned to see the movie tomorrow, until I

3. ### math

A new movie opened the other day. So far, 500,000 people have seen it. The producers of the movie needed to know if the people liked it. A random sample of 8,000 people leaving showings of the movie were asked if they liked the

4. ### Finite

Assume that the producer has 8 skits and 5 commercials available. In how many ways can the producer create a television show?