Suppose that the population P(t) of a country satisfies the differential equationdP= kP(900 – P) with k constant. Its population in 1960 was 300 million and was then growing at thedtrate of 2 million per year. Predict this country's population for the year 2010.This country's population in 2010 will bemillion.(Type an integer or decimal rounded to one decimal place as needed.)

Suppose that the population P(t) of a country satisfies the differential equation = kP(900 – P) with k constant. Its population in 1960 was 300 million and was then growing at the rate of 2 million per year. Predict this country's population for the year 2010. This country's population in 2010 will be million.

Suppose that the population P(t) of a country satisfies the differential equation = kP(900 – P) with k constant. Its population in 1960 was 300 million and was then growing at the rate of 2 million per year. Predict this country's population for the year 2010. This country's population in 2010 will be million.

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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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

Suppose that the population P(t) of a country satisfies the differential equation
dP
= kP(900 – P) with k constant. Its population in 1960 was 300 million and was then growing at the
dt
rate of 2 million per year. Predict this country's population for the year 2010.
This country's population in 2010 will be
million.
(Type an integer or decimal rounded to one decimal place as needed.)

Expert Solution

Step 1

Assume 1960 is the starting year and the population, P is in millions.

So, at $t = 0$ the value of P will be 300.

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ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated