MATH 4A Lecture Notes - Lecture 1: Petri Dish, The Scientists
Document Summary
54 m&ms in a cup are gently tossed onto the table. If a candy lands m side up, it is dead. We removed the dead m&ms and continue with another iteration. Let a(n) be the number of m&ms alive at the end of each iteration. Each side is physically same (blank or m ) So the probability of death for each m is 1/2. a(n+1)=1/2a(n) =(1/2)n+1a(0) a(n)=(1/2)nc is a solution to differential equation. C can be any constant: now we will explore death with immigration. 54 m&ms in a cup are gently tossed onto a table. If a candy lands m side up, it is dead and we will remove it from the population. Then we will add 10 immigrant m&ms back to the population. Let b(n) be the number of m&ms alive at the end of each iteration. =f(n,y n+1 n where f is given and y is un known, is called a first order difference equation. n.
