Suppose that y = y(t) is the size of a population at time t and that the rate of change of the size of the population is proportional to the square of the current size. Note that this is not the exponential growth model. Assume that the initial population is 15. (a) Set up and solve an initial value problem for this model, i.e. find a formula for y(t). Do not forget the constant of proportionality. (b) How long will it take for the population do double in size? Note that your answer will contain the constant of proportionality.

Suppose that y = y(t) is the size of a population at time t and that the rate of change of the size of the population is proportional to the square of the current size. Note that this is not the exponential growth model. Assume that the initial population is 15. (a) Set up and solve an initial value problem for this model, i.e. find a formula for y(t). Do not forget the constant of proportionality. (b) How long will it take for the population do double in size? Note that your answer will contain the constant of proportionality.

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 y = y(t) is the size of a population at time t and that
the rate of change of the size of the population is proportional to the square of the
current size. Note that this is not the exponential growth model. Assume that
the initial population is 15.
(a) Set up and solve an initial value problem for this model, i.e. find a formula for
y(t). Do not forget the constant of proportionality.
(b) How long will it take for the population do double in size? Note that your
answer will contain the constant of proportionality.

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