Competition between bacteria: Suppose there are two types of bacteria, type A and type B, in a place with limited resources. If the bacteria had unlimited resources, both types would grow...

Competition between bacteria: Suppose there are two types of bacteria, type A and type B, in a place with limited resources. If the bacteria had unlimited resources, both types would grow exponentially, with exponential growth rates a for type A and b for type B. Let P be the proportion of type A bacteria, so P is a number between 0 and 1. For example, if P = 0, then there are no type A bacteria and all are of type B. If P = 0.5, then half of the bacteria are of type A and half are of type B. Each population of bacteria grows in competition for the limited resources, so the proportion Pchanges over time. The function P is subject to the equation of change

Suppose a = 2.3 and b = 1.7.

a. Does P have a logistic equation of change?

 b. What happens to the populations if initially P = 0?

 c. What happens to P in the long run if P (0)is positive (but not zero)? In this case, does it matter what the exact value of P (0) is?