The table gives the cumulative sales of iPods since their introduction. Cumulative iPod Sales Year 2003 2004 2005 2006 2007 2008 Sales (million iPods) 0.72 5.636 29.433 66.642 118.672 175.7 (a) Find the function for the quadratic model that gives sales in million iPods, where x is the number of years after 2003, with data from 0 ≤ x ≤ 5. (Round all numerical values to three decimal places.) s(x) = million iPods (b) Write the derivative for the sales model. (Round all numerical values to three decimal places.) s'(x) = million iPods per year (c) Calculate the rate of change of cumulative sales in 2005. (Round your answer to three decimal places.) million iPods per year Interpret the rate of change of cumulative sales in 2005. (Round your answer to three decimal places.) In 2005, cumulative iPod sales were ---Select--- by million per year.

The table gives the cumulative sales of iPods since their introduction. Cumulative iPod Sales Year 2003 2004 2005 2006 2007 2008 Sales (million iPods) 0.72 5.636 29.433 66.642 118.672 175.7 (a) Find the function for the quadratic model that gives sales in million iPods, where x is the number of years after 2003, with data from 0 ≤ x ≤ 5. (Round all numerical values to three decimal places.) s(x) = million iPods (b) Write the derivative for the sales model. (Round all numerical values to three decimal places.) s'(x) = million iPods per year (c) Calculate the rate of change of cumulative sales in 2005. (Round your answer to three decimal places.) million iPods per year Interpret the rate of change of cumulative sales in 2005. (Round your answer to three decimal places.) In 2005, cumulative iPod sales were ---Select--- by million per year.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter3: Straight Lines And Linear Functions

Section3.3: Modeling Data With Linear Functions

Problem 16E: High School Graduates The following table shows the number, in millions, graduating from high school...

See similar textbooks

Related questions

Q: A person invested $530 in an account growing at a rate allowing the money to double every 8 years.…

A: Given problem is : A person invested $530 in an account growing at a rate allowing the money to…

Q: The table to the right shows the average length of a baseball game in minutes for various years.…

Q: The table lists the number of phones sold in millions in the first 5 years on the market. Find a…

Q: Find a quadratic function that models the data below.

A: Consider the quadratic function that model the data is given by y=ax2+bx+c, where a, b and c are…

Q: we that 2-2 = 2x is an explicit function. %3D

A: Explicit function:Explicit functions are functions where one variable is clearly expressed as a…

Q: The area of a sheet of paper is 93.5 square inches. a. Find the remaining, visible area of the sheet…

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: The following graph shows the average candy consumption of a town (in thousands of pounds per year)…

Q: Find a linear function that generates the values in the given table. 3.1 3.2 3.3 3.4 3.5 y 18.4 19.8…

A: Given the table is

Q: The number (in thousands) of women in the work force as function of the year is shown in the figure…

A: Given data A graph of women in the U.S work force from year 1977 to 2017

Q: A college dormitory houses 650 students, all of whom are susceptible to a particular infectious…

A: Step 1:To find a function that gives the number of students who have contracted the virus at any…

Q: A farmer wishes to build a divided pasture adjacent to the river, as shown in the diagram.…

A: Let y be the side of the fence that is parallel to the border of the river side and x be the length…

Q: the operating expesnes of amazon increased from 3.6 billion in 2008 to 16.3 billion in 2012. use the…

A: Given that The operating expenses of amazon increased from 3.6 billion in 2008 to 16.3 billion in…

Q: A user is charged P500.00 monthly for a particular mobile plan, which includes P150.00 free text…

Q: The figure shows a page with 1-inch margins at the top and the bottom and half-inch side margins. A…

A: Let the length and width of the printed page be y and x, respectively. Given printed area of page is…

Question

The table gives the cumulative sales of iPods since their introduction.
Cumulative iPod Sales
Year
2003
2004
2005
2006
2007
2008
Sales
(million iPods)
0.72
5.636
29.433
66.642
118.672
175.7
(a) Find the function for the quadratic model that gives sales in million iPods, where x is the number of years after 2003, with data from 0 ≤ x ≤ 5. (Round all numerical values to three decimal places.)
s(x) =
million iPods
(b) Write the derivative for the sales model. (Round all numerical values to three decimal places.)
s'(x) =
million iPods per year
(c) Calculate the rate of change of cumulative sales in 2005. (Round your answer to three decimal places.)
million iPods per year
Interpret the rate of change of cumulative sales in 2005. (Round your answer to three decimal places.)
In 2005, cumulative iPod sales were ---Select--- by
million per year.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

(a)

(b)

(c)

Step by step

Solved in 4 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

What is regression analysis? Describe the process of performing regression analysis on a graphing utility.
High School Graduates The following table shows the number, in millions, graduating from high school in the United States in the given year. Year Number graduating in millions 1985 2.83 1987 2.65 1989 2.47 1991 2.29 a. By calculating difference, show that these data can be modeled using a linear function. b. What is the slope for the linear function modeling high school graduations? Explain in practical terms the meaning of the slope. c. Find a formula for a linear function that models these data. d. Express, using functional notation, the number graduating from high school in 1994, and then use your formula from part c to calculate that value.
How do you find the value of a function?
The number of people afflicted with the common cold in the winter months dropped steadily by 50 each yearsince 2004 until 2010. In 2004, 875 people were inflicted. Find the linear function that models the number of people afflicted with the common cold C as a function of theyear, t. When will no one be afflicted?
Table 6 shows the year and the number ofpeople unemployed in a particular city for several years. Determine whether the trend appears linear. If so, and assuming the trend continues, in what year will the number of unemployed reach 5 people?
A user is charged P500.00 monthly for a particular mobile plan, which includes P150.00 free text messages. Messages in excess of 150 are charged P1.00 each. Represent the amount a consumer pays each month as a function of the number of messages m sent in a month.
Evaluate the function to answer the question. Botanists have determined that some species of weed grow in a circular pattern. For one such species, the area A, in square meters, can be approximated by A(t) = 0.0067nt^2, where t is the time in days after the growth of the weed first can be observed. Find the area (in square meters) this weed will cover 100 days after the growth is first observed. Round to the nearest square meter. ? m^2
A block is hanging on a spring. The length of the spring is a Mass Length linear function of the mass of the block. The table shown to the (grams) (Centimeters) right lists the length of the spring resulting from suspending 5 27 each of the three blocks. What is the length of the spring in 35 centimeters when an 11 gram block is suspended from it? 15 47 (A) 31 (B) 36 (C) 39 (D) 41 (E) 45
We opened this section with a study showing that late in the semester, procrastinating students reported more symptoms of physical illness than their nonprocrastinating peers.a. At the beginning of the semester, procrastinators reported an average of 0.8 symptoms, increasing at a rate of 0.45 symptoms per week. Write a function that models the average number of symptoms after x weeks.b. At the beginning of the semester, nonprocrastinators reported an average of 2.6 symptoms, increasing at a rate of 0.15 symptoms per week. Write a function that models the average number of symptoms after x weeks.c. By which week in the semester did both groups report the same number of symptoms of physical illness? For that week, how many symptoms were reported by each group?How is this shown in Figure.