My year 12 Specialist students are working on logistic growth at the moment. An example might be helpful.
A new viral disease was found to spread according to the equation , where is the susceptible population, is the number of people infected at time months and . In March 2010, it was thought only 100 people out of a population of 18 million were infected. Use the logistic model to find the number infected in:
(a) March 2011
(b) June 2012
(c) January 2017
Specialist 12 – Nelson Senior Maths
Use partial fractions to separate the denominator
When
When
Let and rearrange to make the subject.
Divide by
Initially 100 people were infected.
(a) , hence
(b) , hence
(c) , hence .
It is not necessary to solve the differential equation, you can use the formula
This formula is on the Year 12 Mathematics Specialist formula sheet for Western Australia.
For our question,
So,
And you can substitute values for .