A new chapter in maths was introduced to me and i have difficulities understanding it. On the presentation of an example it states that if the population growth of bacterias are for example y'=2y than y=e^2x. problem is that if the mass of the bacteria is 10^15kg than after 48h the total mass of the bacterias would be 5*10^26kg which the book states doesnt make sense and i agree. Now they introduce the limiting factor so that the rate of the growth is decreased when the population is increasing. The introduce the the logical growthmodel where you plug in (1-y/M)
y'=kq(1-y/M) where M is the maximal size of the population. They state that our math skills is not enough to solve the differential equations so we have to accept that when y=M/2 then y'=max value. Now my on a question when i apply this i dont get the same answer as the textbook. the question states.
The maximal number of sick people in an epidimi is 6000. and is growing according to the logical growthequation with the konstant 0.0004. what is the formula for the equation?
My attempt of the solution: y'=0.0004y(1-y/6000). y(0)=0 Now the book states y'=0.0004y(6000-y) which i find weird since its not the logical growthmodel that they introduce in this chapter.
Thankful for all help.