User:Vishnukanduri/MY PROJECT

 WIKI DESCRIBING MY PROJECT 

''' COURSE SC107: WHERE ARE YOU? FALL 2016 '''

 ASSIGNED BY: 

 PROFESSOR MANISH .K. GUPTA 

 DAIICT 

 GANDHINAGAR 

 INDIA 

My topic is Logistic growth where calculus is applied and has many applications in our everyday life. It also has great applications in the field of medicine, biology, ecology and many more fields. I will be describing about Logistic growth and logistic function and the differential equation involved in it and how to solve it.

There are two types of growths that can occur in a region of population. They are exponential logistic growth and logistic growth. Logistic growth occurs when the resources available are depleting and are not able to suffice the population and the growth rate decreases as the population reaches carrying capacity. Carrying capacity is the maximum number of individuals that the environment can support. Suppose the population has an upper bound M.

Let 0<y(t)<M. Then,

The rate of change of population is directly proportional to the population and the difference between the population and maximum. Then the proportionality symbol can be replaced by an equality sign multiplying by a constant. This constant is called as PER CAPITA GROWTH RATE. Then we arrive at a differential equation which can be solved by the method of separation of variables which is quite simple and basic. We arrive at a solution which can be understood better by varying the different constants. I would like to give an interesting example to illustrate the application of logistic growth.

If a rumor is spreading at a college that has a given population. If a certain number of people know the rumor initially and after some days if some number of people know the rumor. We can calculate how many number of people would know the rumor on a given day and many more applications like these.