There once was a small paramecium. This paramecium was brave, and it left its home on a journey to find the Promised Land! For you see, this paramecium had grown up learning from its elders about the existence of a land full of space and resources, where a young paramecium can grow at a rate proportional to the size of the population. Now, our young paramecium seeks this land for it and all of its kind to grow at an unlimited rate. (a) Write a differential equation that would describe the paramecium's growth. (Note: we're not looking for a solution yet, just the differential equation.) (b) If this young paramecium finds its way to the Promised Land, it will begin consuming resources at a massive rate, enough for the paramecium to eventually split itself into two! Suppose after 5 hours, there are now 32 paramecia in the Promised Land. Based on this information, solve for the constant of proportionality k and write a model that will give the total number of paramecia after t hours. (c) Does it make sense that a true "Promised Land" would exist for the paramecium? Why or why not?