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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 P 0.0051 dt 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. O P(t) Po e0.0051t P(t) = Poe0.0051t P(t) = Poe0.0051t – pPo %3D e0.0051t P(t) = Po O P(t) = Poe0.0051t + 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) = (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

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 0.0051 dt 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. O P(t) Po e0.0051t P(t) = Poe0.0051t P(t) = Poe0.0051t – pPo %3D e0.0051t P(t) = Po O P(t) = Poe0.0051t + 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) = (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

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 16EQ
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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 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. Po P(t) e0.0051t P(t) = Poe0.0051t P(t) = Pe0.0051t - P. e0.0051t P(t) Po O P(t) = Poe0.005it + Po (c) Find the particular solution of the differential equation if in 2010 (t = 0), the population of China was 1.341335 x 10°. %3D P(t) = (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
Transcribed Image Text: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 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. Po P(t) e0.0051t P(t) = Poe0.0051t P(t) = Pe0.0051t - P. e0.0051t P(t) Po O P(t) = Poe0.005it + Po (c) Find the particular solution of the differential equation if in 2010 (t = 0), the population of China was 1.341335 x 10°. %3D P(t) = (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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