During the period from 1790 to 1930, the U.S. population P(t) (t in years) grew from 3.9 million to 123.2 million. Throughout this period, P(t) remained close to the solu- tion of the initial value problem dP = 0.03135P – 0.0001489P², P(0) = 3.9. dt (a) What 1930 population does this logistic equation pre- dict? (b) What limiting population does it predict? (c) Has this logistic equation continued since 1930 to ac- curately model the U.S. population? [This problem is based on a computation by Verhulst, who in 1845 used the 1790–1840 U.S. population data to pre- dict accurately the U.S. population through the year 1930 (long after his own death, of course).] sOwn
During the period from 1790 to 1930, the U.S. population P(t) (t in years) grew from 3.9 million to 123.2 million. Throughout this period, P(t) remained close to the solu- tion of the initial value problem dP = 0.03135P – 0.0001489P², P(0) = 3.9. dt (a) What 1930 population does this logistic equation pre- dict? (b) What limiting population does it predict? (c) Has this logistic equation continued since 1930 to ac- curately model the U.S. population? [This problem is based on a computation by Verhulst, who in 1845 used the 1790–1840 U.S. population data to pre- dict accurately the U.S. population through the year 1930 (long after his own death, of course).] sOwn
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...
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![During the period from 1790 to 1930, the U.S. population
P(t) (t in years) grew from 3.9 million to 123.2 million.
Throughout this period, P(t) remained close to the solu-
tion of the initial value problem
dP
= 0.03135P – 0.0001489P², P(0) = 3.9.
dt
(a) What 1930 population does this logistic equation pre-
dict?
(b) What limiting population does it predict?
(c) Has this logistic equation continued since 1930 to ac-
curately model the U.S. population?
[This problem is based on a computation by Verhulst, who
in 1845 used the 1790–1840 U.S. population data to pre-
dict accurately the U.S. population through the year 1930
(long after his own death, of course).]
sOwn](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd995f1a0-b392-4129-86d5-33b065590456%2F012d791d-5e80-40c7-bb2a-3239cdb27d97%2Fb7s6q1r.png&w=3840&q=75)
Transcribed Image Text:During the period from 1790 to 1930, the U.S. population
P(t) (t in years) grew from 3.9 million to 123.2 million.
Throughout this period, P(t) remained close to the solu-
tion of the initial value problem
dP
= 0.03135P – 0.0001489P², P(0) = 3.9.
dt
(a) What 1930 population does this logistic equation pre-
dict?
(b) What limiting population does it predict?
(c) Has this logistic equation continued since 1930 to ac-
curately model the U.S. population?
[This problem is based on a computation by Verhulst, who
in 1845 used the 1790–1840 U.S. population data to pre-
dict accurately the U.S. population through the year 1930
(long after his own death, of course).]
sOwn
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Step 1: Introduce to the given information
VIEWStep 2: Determining the solution of the differential equation
VIEWStep 3: Determining the value of C_1 and finding the function P in terms of t
VIEWStep 4: (a) Determining the population in 1930 using logistics equation
VIEWStep 5: (b) Determining the limiting population
VIEWStep 6: (c) Explaining if logistic equation accurately model the U.S. population since 1930
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