A certain nature reserve can support no more than 4000 mountain goats. Assume that the rate of growth is proportional to how close the population is to this maximum, with a growth rate of 20 percent. There are currently 1000 goats in the area. (a) Solve the general limited growth differential equation, and then write a function describ- ing the goat population at time t. (b) What will the goat population be in 5 years?

A certain nature reserve can support no more than 4000 mountain goats. Assume that the rate of growth is proportional to how close the population is to this maximum, with a growth rate of 20 percent. There are currently 1000 goats in the area. (a) Solve the general limited growth differential equation, and then write a function describ- ing the goat population at time t. (b) What will the goat population be in 5 years?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.7: Applications

Problem 13EQ

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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.

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(a) Solve the general limited growth differential equation, and then write a function describ- ing the goat population at time t.

(b) What will the goat population be in 5 years?

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

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