The table gives the increase or decrease in the number of donors to a college athletics support organization for selected years.Rate of Change of Donors to a College AthleticsSupport OrganizationYear1985=19881991199419972000Rate of change(donors per year)-17678512131079408-836(a) Find the function of the quadratic model that gives the rate of change in number of donors, where t is the number of years since 1985, with data from 0 ≤ t ≤ 15. (Round all numerical values to three decimal places.)f'(t) =donors per year(b) Find the function of the model that gives the number of donors, where t is the number of years since 1985. Use the fact that in 1990, there were 10,706 donors. (Round all numerical values to three decimal places.)f(t)donors(c) Estimate the number of donors in 2004. (Round your answer to the nearest integer.)donors

Since year started from 1985, taking year,t=0 for 1985 make a table accordingly: Time Year, t…

Answered: The table gives the increase or…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Demand Function At $5 each, 300 hats will be sold. But at $3 each, 800 hats will be sold. Express the number of hats sold as a linear function of the price per hat.
The growth rate of the speed of sound in relation to the temperature in degrees Fahrenheit is a linear function. The speed of sound at 0 degrees Fahrenheit is 1052.3 feet per second. For every 1 degree Fahrenheit rise in temperature, the speed of sound increases by 1.1 feet per second. A. Identify the initial value of linear function that gives the speed of sound in terms of temperature. B. A 20 degree Fahrenheit rise in temperature would provide what increase in the speed of sound? C. What would the speed of sound be after a 67 degree Fahrenheit rise in temperature?
The cost �(�), where � is the number of miles driven, of renting a car for a day is $41 plus $1.75 per mile.What is the slope of the linear function and its units? What is the �-intercept and its units? What is the linear function, �(�)?
A company mines low-grade nickel ore. If the company mines x tons of ore, it can sell the ore for p = 270 - 0.45x dollars per ton. a. Find the domain of p. b. Express the revenue as a function of x. c. How many tons of ore should the company mine to achieve the maximum revenue? What is the maximum revenue?
A company buys a new bulldozer for $92050. The company depreciates the bulldozer linearly over its useful life of 17 years. Its salvage value at the end of 17 years is $12150. Depreciation is the decrease or loss in value of the equipment due to age, wear, or market conditions. Express the value of the bulldozer, V, in terms of how many years old it is, t. V=______________ The value of the bulldozer after 5 years is $______________
World grain production was 1,241 million tons in 1975 and 2,048 million tons in 2005, and has been increasing at an approximately constant rate. (a) Find a linear function for world grain production, P, in million tons, as a function of t, the number of years since 1975.
U.S. Population Over Age 16 The table gives theprojections of the population, in millions, of U.S.residents over age 16 for selected years 2015 to 2060.a. Graph the data, with y equal to the population inmillions and x equal to the number of years after2010.b. Find a linear function that models the data, with yequal to the population in millions and x equal to thenumber of years after 2010.c. Graph the model and the data on the same axesand comment on the fit of the model to the data.d. What does the model predict that the populationwill be in 2042?e. In what year does the model predict that the population will be 336.827 million?
Coal Consumption The following table gives the amount of coal (in thousand short tons) consumed by U. S. utilities to pro- duce electricity. Source: U.S. Department of Energy. Year Consumption 1995 850 2000 986 2005 1037 2010 934 2012 825 (a) Plot the data by letting t be the years since 1990. Would a linear or quadratic function model these data best? (b) Find the quadratic function defined by f(t) = a(t – h)? + k that models the data. Use the highest point as the vertex, (h, k). Then choose (10, 986) as a second point to determine a.
In 2005 the average annual and fees for attending a private college or university was $22000. This cost rose to about $36000 in 2015, as illustrated in the graph. Complete parts a and b
A dairy spends $24,000 per year to maintain its barns and equipment. It costs $2000 per year to feed and care for each dairy cow. (a) Using C for the number of dairy cows and E for the total yearly expense, in dollars, find a formula that gives the total yearly expense as a linear function of the number of dairy cows. E = (b) Use functional notation to express the total expense if the dairy has 40 cows. E(40) E(40C) 40E E(2000) E(24,000) (c) Calculate the value from part (b). $

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS