Advanced Engineering Mathematics, 7th Edition

2.7 Linear Models

INTRODUCTION

In this section we solve some of the linear first-order models that were introduced in Section 1.3.

Growth and Decay

The initial-value problem

(1)

where k is the constant of proportionality, serves as a model for diverse phenomena involving either growth or decay. We have seen in Section 1.3 that in biology, over short periods of time, the rate of growth of certain populations (bacteria, small animals) is observed to be proportional to the population present at time t. If a population at some initial time t₀ is ...