A news item is spreading by word of mouth through a population of size 40,000 people. After t days, the number of people (in thousands) who have heard the news is given by the following equation. y = f(t) 40 1+50e-16 (a) Approximately how many thousand people have heard the news after 9 days? (Give your answer correct to at least three decimal places.) thousand people (b) Calculate the derivative f(t). r(t) = (c) At what rate is the news spreading after 10 days? (Give your answer correct to at least four decimal places.) thousand people per day
A news item is spreading by word of mouth through a population of size 40,000 people. After t days, the number of people (in thousands) who have heard the news is given by the following equation. y = f(t) 40 1+50e-16 (a) Approximately how many thousand people have heard the news after 9 days? (Give your answer correct to at least three decimal places.) thousand people (b) Calculate the derivative f(t). r(t) = (c) At what rate is the news spreading after 10 days? (Give your answer correct to at least four decimal places.) thousand people per day
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A news item is spreading by word of mouth through a population of size 40,000 people. After t days, the number of people (in thousands) who have
heard the news is given by the following equation.
y = f(t)
(a) Approximately how many thousand people have heard the news after 9 days? (Give your answer correct to at least three decimal
places.)
thousand people
40
1+50e-16
(b) Calculate the derivative f(t).
f(t) =
(c) At what rate is the news spreading after 10 days? (Give your answer correct to at least four decimal places.)
thousand people per day
(d) Compare the function f(t) to the solutions to the different forms of the logistic growth model from this lesson. Enter the differential
equation in terms of y that corresponds to this solution.
dy
dt
=
(e) How many people have heard the news when its rate of spread is 15.96 thousand people per day? (There are two answers. Give your
answers correct to the nearest whole person.)
people (smaller value)
people (larger value)
(f) At what two times is the news spreading at rate 15.96 thousand people per day? (Give your answers correct to at least three decimal
places.)
days (smaller value)
days (larger value)
(9) What is the fastest rate at which the news spreads? (Give your answer correct to at least three decimal places.)
thousand people per day
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