After carefully thinking through these problems, print out this file and write in your solutions clearly, with work shown. Scan the document to create a single PDF file to hand in on our D2L site under Assessments Assignments Wk 3 HW. 1. The following differential equation gives another model similar to the logistic model. dP dt kP(InM - InP); k, M constants a. Assume all quantities are positive, and M > P. M still represents the carrying capacity. Show that with this model, the curve has an inflection point when P = M. So, the rate of growth slows down "sooner" than it would using the logistic growth model. Note: to do this, you need to show that the second derivative of Pw.r.t. t changes sign when P = M