Between 2006 and 2016, the number of applications for patents, N, grew by about 4.1% per year. That is, N'(t) = 0.041N(t). a) Find the function that satisfies this equation. Assume that t = 0 corresponds to 2006, when approximately 454,000 patent applications were received. b) Estimate the number of patent applications in 2020. c) Estimate the rate of change in the number of patent applications in 2020. a) N(t) = b) The number of patent applications in 2020 will be (Round to the nearest whole number as needed.) c) The rate of change in the number of patent applications in 2020 is about (Round to the nearest whole number as needed.) year(s) per application. application(s) per year.
Between 2006 and 2016, the number of applications for patents, N, grew by about 4.1% per year. That is, N'(t) = 0.041N(t). a) Find the function that satisfies this equation. Assume that t = 0 corresponds to 2006, when approximately 454,000 patent applications were received. b) Estimate the number of patent applications in 2020. c) Estimate the rate of change in the number of patent applications in 2020. a) N(t) = b) The number of patent applications in 2020 will be (Round to the nearest whole number as needed.) c) The rate of change in the number of patent applications in 2020 is about (Round to the nearest whole number as needed.) year(s) per application. application(s) per year.
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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(12) Please show work for parts b and c
Transcribed Image Text:Between 2006 and 2016, the number of applications for patents, N, grew by about 4.1% per year. That is,
N'(t) = 0.041N(t).
a)
Find the function that satisfies this equation. Assume that t = 0 corresponds to 2006, when approximately 454,000
patent applications were received.
b) Estimate the number of patent applications in 2020.
c) Estimate the rate of change in the number of patent applications in 2020.
a) N(t) =
b) The number of patent applications in 2020 will be
(Round to the nearest whole number as needed.)
c) The rate of change in the number of patent applications in 2020 is about
(Round to the nearest whole number as needed.)
year(s) per application.
application(s) per year.
Expert Solution
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Between 2006 and 2016, the number of applications for patents, N, grew by about 4.1% per year. That is, N'(t)=0.041N(t).
a) Find the function that satisfies this equation. Assume that t = 0 corresponds to 2006, when approximately 454,000 patent applications were received.
b) Estimate the number of patent applications in 2020.
c) Estimate the rate of change in the number of patent applications in 2020.
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