please answer from your own work on a paper providing all steps for good feedback.

4-. Now let's assume that there is a minimum number m that a population must have in order to survive over many generations. Any society with fewer than m people will experience a negative growth rate. Any society with more than 11': people will experience a pm growth rate. Any society with exactly m people will have a growth rate of zero. To model this. we don't need a completely new di'erential equation. We just need an improvement on the previous equation one that factors in this new information. a] Show using notation what the paragraph ahove explains in three separate cases {when P s: m,when P 2: m, and when P = m]. h] Design a factor that will achieve this effect and write out the improved differential equation. 5. Let's take one more step in improving this population model. Assume that there is a maximum number M thata population can sustain in order to survive over many generations. After all, there are limited resources in our world. When the population size is much smaller than M, resources playr a negli'hle role in determining the population growth rate. When the population size exceeds M. it experiences a negative growth rate. When the population size equals M, the population growth rate equals zero. a] Show using notation what the paragraph ahove explains in three separate cases {when P sf. M. when P 2::- M. andwhenP = M]. h] Design a factor that will achieve this effect and write out the improved differential equation. c] Draw the family of comes that represent P in relation to t