The population of a community is known to increase at a rate proportional to the number of people present at time t. If an initial population P0 has doubled in 5 years, how long will it take to triple? To quadruple?

Question.

 

The population of a community is known to increase at a rate proportional to the number of people present at time t. If an initial population P₀ has doubled in 5 years, how long will it take to triple? To quadruple?

 

Solution:

 

<![if !msEquation]><![endif]>

Initial population doubled in five years i.e. <![if !msEquation]><![endif]>

 

Put initial condition <![if !msEquation]><![endif]> in <![if !msEquation]><![endif]>

<![if !msEquation]><![endif]>

<![if !msEquation]><![endif]>

<![if !msEquation]><![endif]>

<![if !msEquation]><![endif]>

Therefore, <![if !msEquation]><![endif]>

 

Time required for population to triple i.e. <![if !msEquation]><![endif]>

<![if !msEquation]><![endif]>

<![if !msEquation]><![endif]>

<![if !msEquation]><![endif]>

<![if !msEquation]><![endif]>   (nearly 8 years)

 

Time required for population to quadruple i.e. <![if !msEquation]><![endif]>

<![if !msEquation]><![endif]>

<![if !msEquation]><![endif]>

<![if !msEquation]><![endif]>

<![if !msEquation]><![endif]>             (approximately 10 years)