dPSuppose that the population P(t) of a country satisfles the differential equation kP(400 - P) with k constant.population in 1960 was 200 million and was then growing at the rate of 3 million per year. Predict this country's population for the year2020.This country's population in 2020 will be milion.(Type an integer or decimal rounded to one decimal place as needed.)

Suppose that the population Pt) of a country satisfies the differential equation P(400 - P) with k constant. Its population in 1960 was 200 milion and was then growing at the rate of 3 milion per year, Predict this country's population for the year 2020. This country's populasion in 2020 wil be milion. (Type an integer or decimal rounded to one decimal place as needed.)

Suppose that the population Pt) of a country satisfies the differential equation P(400 - P) with k constant. Its population in 1960 was 200 milion and was then growing at the rate of 3 milion per year, Predict this country's population for the year 2020. This country's populasion in 2020 wil be milion. (Type an integer or decimal rounded to one decimal place as needed.)

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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Question

dP
Suppose that the population P(t) of a country satisfles the differential equation kP(400 - P) with k constant.
population in 1960 was 200 million and was then growing at the rate of 3 million per year. Predict this country's population for the year
2020.
This country's population in 2020 will be milion.
(Type an integer or decimal rounded to one decimal place as needed.)

Expert Solution

Step 1

It is given that population P(t) satisfies the differential equation-

$\frac{d P}{d t} = k P (400 - P) - (1)$

Also given that -

$P (0) = 200 m i l l i o n a n d \frac{d P (0)}{d t} = 3 S i n c e t = 0 f o r 1960 y e a r . W e h a v e t o f i n d p o p u l a t i o n i n 2020 y e a r . T h a t i s, P (60) F o r 2020 y e a r t = 60$