Barring disasters (human-made or natural), the population P of humans grows at a rate proportional to its current size. According to the U.N. World Population studies, from 2005 to2010 the population of China grew at an annual rate of 0.510% per year.(a) Write a differential equation that models the growth rate of the population.dPPdt0.0051dP= 0.0051PdtdP= P(0.0051 + 1)dtdP= P(0.0051 – 1)dtdP0.0051dt(b) Find the general solution of the differential equation.P(t) = Poe0.005+ PoPoe0.0051tP(t)P(t) = Poe0.0051tP(t) = Poe0.0051t – P.e0.0051tP(t) :(c) Find the particular solution of the differential equation if in 2010 (t = 0), the population of China was 1.341335 × 10°.P(t) =%3D(d) If the rate of growth continues to follow this model, how many years will be needed for population of China reach 2.9 billion persons? (Round your answer to three decimalplaces.)years

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Barring disasters (human-made or natural), the population P of humans grows at a rate proportional to its current size. According to the U.N. World Population studies, from 2005 to 2010 the population of China grew at an annual rate of 0.510% per year. (a) Write a differential equation that models the growth rate of the population. dP %3D dt 0.0051 dP = 0.0051P dt dP = P(0.0051 + 1) dt dP = P(0.0051 - 1) dt 0.0051 %3D dt (b) Find the general solution of the differential equation. O P(t) = Poe0.0051t + Po Po O P(t) = e0.0051t O P(t) = Poe0.0051t O P(t) = Poe0.0051t – Po e0.0051t O P(t) = Po (c) Find the particular solution of the differential equation if in 2010 (t = 0), the population of China was 1.341335 x 10°. P(t) =

Barring disasters (human-made or natural), the population P of humans grows at a rate proportional to its current size. According to the U.N. World Population studies, from 2005 to 2010 the population of China grew at an annual rate of 0.510% per year. (a) Write a differential equation that models the growth rate of the population. dP %3D dt 0.0051 dP = 0.0051P dt dP = P(0.0051 + 1) dt dP = P(0.0051 - 1) dt 0.0051 %3D dt (b) Find the general solution of the differential equation. O P(t) = Poe0.0051t + Po Po O P(t) = e0.0051t O P(t) = Poe0.0051t O P(t) = Poe0.0051t – Po e0.0051t O P(t) = Po (c) Find the particular solution of the differential equation if in 2010 (t = 0), the population of China was 1.341335 x 10°. P(t) =

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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Barring disasters (human-made or natural), the population P of humans grows at a rate proportional to its current size. According to the U.N. World Population studies, from 2005 to
2010 the population of China grew at an annual rate of 0.510% per year.
(a) Write a differential equation that models the growth rate of the population.
dP
P
dt
0.0051
dP
= 0.0051P
dt
dP
= P(0.0051 + 1)
dt
dP
= P(0.0051 – 1)
dt
dP
0.0051
dt
(b) Find the general solution of the differential equation.
P(t) = Poe0.005
+ Po
Po
e0.0051t
P(t)
P(t) = Poe0.0051t
P(t) = Poe0.0051t – P.
e0.0051t
P(t) :
(c) Find the particular solution of the differential equation if in 2010 (t = 0), the population of China was 1.341335 × 10°.
P(t) =
%3D
(d) If the rate of growth continues to follow this model, how many years will be needed for population of China reach 2.9 billion persons? (Round your answer to three decimal
places.)
years

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