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3. Let P representthe size of a population and let I represent lime. a] Explain how l[he size of a population aifects its growth rate, assuming a large enough starting population and unlimited resom'ces. For example, imagine if humans were separated into three separate regions of the world. with population sizes llili. 200.001]. and 300,001]. How would the growth rates of these societies compare to each other? b] Based on this. express the population growth rate as a differential equation. 4-. Now leifs 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 in people will experience a negative growth rate. Any society with more than in people will experienoe a pm growth rate. Any society with exactly 111 people will have a growth rate of zero. To model this. we don't need a completely new differential equation We just need an improvement on the previous equation one that zcors in this new information. a] Show using notation what the paragraph above explains in three separate cases {when P If. m,when P I} m. and when P = m]. b] Design a factor lIhat will achieve this effect and write out the improved differential equation