The projected number of senior citizens in the U.S. for the years 1995 through 2030 can be modeled by N(X), million senior citizens, where x is the number of years after 2000. N(X) = 0.03x² + 0.315x + 34.23 (a) Find the derivative of N(x) and use it to complete the model statement below. (Refer back to Section 3.2 of your text (or ebook) for simple derivative rules.) N'(x)= 2030. --select units-- gives the projected rate at which the number of senior citizens is changing x years after 2000, for the years 1995 through Use the appropriate function from above to answer questions b through d. (b) What is the projected number of senior citizens in the year 2025? (Round your answers to 3 decimal places.) million senior citizens (c) What is the projected rate of change of the number of senior citizens in 2025? (Round your answers to 3 decimal places.) million senior citizens per year (d) The Census Bureau predicts that in 2030, 20.1% of the U.S. population will be senior citizens. Use this prediction to estimate the total U.S. population in 2030. (Round your answer to 3 decimal places.) million people

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...
icon
Related questions
Question
Quantity vs. Rate-of-Change
The projected number of senior citizens in the U.S. for the years 1995 through 2030 can be modeled by N(x), million senior citizens, where x is the number of years after 2000.
N(x) = 0.03x2 + 0.315x + 34.23
(a) Find the derivative of N(x) and use it to complete the model statement below. (Refer back to Section 3.2 of your text (or ebook) for simple derivative rules.)
N'(x)=
--select units--
O gives the projected rate at which the number of senior citizens is changing x years after 2000, for the years 1995 through
2030.
Use the appropriate function from above to answer questions b through d.
(b) What is the projected number of senior citizens in the year 2025? (Round your answers to 3 decimal places.)
million senior citizens
(c) What is the projected rate of change of the number of senior citizens in 2025? (Round your answers to 3 decimal places.)
million senior citizens per year
(d) The Census Bureau predicts that in 2030, 20.1% of the U.S. population will be senior citizens. Use this prediction to estimate the total U.S. population in 2030. (Round your
answer to 3 decimal places.)
million people
Transcribed Image Text:Quantity vs. Rate-of-Change The projected number of senior citizens in the U.S. for the years 1995 through 2030 can be modeled by N(x), million senior citizens, where x is the number of years after 2000. N(x) = 0.03x2 + 0.315x + 34.23 (a) Find the derivative of N(x) and use it to complete the model statement below. (Refer back to Section 3.2 of your text (or ebook) for simple derivative rules.) N'(x)= --select units-- O gives the projected rate at which the number of senior citizens is changing x years after 2000, for the years 1995 through 2030. Use the appropriate function from above to answer questions b through d. (b) What is the projected number of senior citizens in the year 2025? (Round your answers to 3 decimal places.) million senior citizens (c) What is the projected rate of change of the number of senior citizens in 2025? (Round your answers to 3 decimal places.) million senior citizens per year (d) The Census Bureau predicts that in 2030, 20.1% of the U.S. population will be senior citizens. Use this prediction to estimate the total U.S. population in 2030. (Round your answer to 3 decimal places.) million people
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 6 steps

Blurred answer
Knowledge Booster
Differential Equation
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning