Advanced Physics In a given location, the deer population in 2000 was estimated around 509,000 and in 2001 was estimated around 674,500. Wildlife managers believe the region can sustain up to 10 million deer (i.e., A = 10 x106). The model for the population growth in this location is: dP dt = kP (A P ). (a) Use the method of separation to solve for P (t) from the differential equation. (b) Use the initial conditions to solve for C and insert it into the equation you found in part (a). (c) What is the population going to be in 4 years? (d) Approximately how long will it take for the population to near its population cap (when will Pit) be close to 10 x106)? Justify your